Solutions and Justifying Your Work ___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Prerequisite Skills Needed: - Order of Operations - Algebraic Properties Previous Video: Equations w/Variables on Both Sides

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4x – 6 = x + 9 Solutions and Justifying Your Work We earlier solved this equation

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4x – 6 = x + 9 Solutions and Justifying Your Work 3x = 15 -1x = -x 3x – 6 = = + 6 x = 5 3 = 3 We earlier solved this equation and got x = 5 for the solution.

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. 4x – 6 = x + 9

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. 4x – 6 = x + 9 We earlier solved this equation and got x = 5 for the solution. Don’t Forget to follow Order of Operations (PEMDAS)!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work = So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. 4x – 6 = x + 9 We earlier solved this equation and got x = 5 for the solution. Don’t Forget to follow Order of Operations (PEMDAS)!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work = So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. 4x – 6 = x = 14 Because we ended up with a TRUE statement -(it is true that 14 equals 14)- then we have PROVED that x = 5 for this equation! Great job! We earlier solved this equation and got x = 5 for the solution.

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ An important part of math is being able to justify your solutions. You gotta PROVE you know what you’re doing! One way to do this is by understanding how solutions complete an equation. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work = So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. 4x – 6 = x = 14 Because we ended up with a TRUE statement -(it is true that 14 equals 14)- then we have PROVED that x = 5 for this equation! Great job! We earlier solved this equation and got x = 5 for the solution. It is ALWAYS a good idea to check your solutions!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Here’s a way to see it visually as well: Solutions and Justifying Your Work 4x – 6 = x xxxxx Remember to keep the sides balanced. x = 5

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Here’s a way to see it visually as well: Solutions and Justifying Your Work 4x – 6 = x xxxxx x = 5

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Here’s a way to see it visually as well:. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work 4x – 6 = x x = 5

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Here’s a way to see it visually as well:. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work 4x – 6 = x = x = 5

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Here’s a way to see it visually as well:. 4(5) – 6 = (5) + 9 Solutions and Justifying Your Work 4x – 6 = x = = 14 x = 5

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Steps Reasons (What step did you take?)(How do you know you can do that?)

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?)

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) Break each step down and state the rule that allows you to perform that math operation.

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x x =-1x 3x – 6 = 9 Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x x =-1x 3x – 6 = 9 Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x x =-1x 3x – 6 = 9 Given information Subtraction Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x x =-1x 3x – 6 = 9 Given information Subtraction Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = + 6 Given information Subtraction Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = + 6 Given information Subtraction Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = + 6 Given information Subtraction Prop. of Equality Addition Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = = 3 Given information Subtraction Prop. of Equality Addition Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = = 3 Given information Subtraction Prop. of Equality Addition Prop. of Equality Division Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ You should also be able to state the Algebraic Properties that prove each step. Solutions and Justifying Your Work Prove that x = 5 when 4x – 6 = x + 9. Many students get stuck on this, but don’t let it fluster you! Steps Reasons (What step did you take?)(How do you know you can do that?) 4x – 6 = x + 9 3x = 15 -1x =-1x 3x – 6 = = + 6 x = 5 3 = 3 Given information Subtraction Prop. of Equality Addition Prop. of Equality Division Prop. of Equality Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?)

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information 3(x + 2) = - 5 – 2(x - 3)

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 Distributive Property

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x (-5) Distributive Property

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x (-5) Distributive Property

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x + 1 3x + 6 = – 2x (-5) Distributive Property

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x + 1 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = + 1 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = + 1 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = - 5 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality Subtraction Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = - 5 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality Subtraction Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = = 5 3x + 6 = – 2x (-5) Distributive Property Addition

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality Subtraction Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = = 5 3x + 6 = – 2x (-5) Distributive Property Addition Division Prop. of Equality

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality Subtraction Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = = 5 x = - 1 3x + 6 = – 2x (-5) Distributive Property Addition Division Prop. of Equality

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solutions and Justifying Your Work Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. Steps Reasons (What step did you take?)(How do you know you can do that?) Given information Commutative Prop. Of Addition Addition Prop. of Equality Subtraction Prop. of Equality 3(x + 2) = - 5 – 2(x - 3) 3x + 6 = - 5 – 2x + 6 3x + 6 = – 2x x = +2x 5x + 6 = = - 6 5x = = 5 x = - 1 3x + 6 = – 2x Distributive Property Addition Division Prop. of Equality NOW WHAT? 1 ) Re-watch/Re-wind 2) Master Practice Problems 3) Next Skill: Translating Words Into Expressions & Equations

___________________________________________________ __________ Algebra 1 – Solving Equations - Math is Hip ™ Solving Equations w/Variables on Both Sides Here are some more examples – this time without the use of the balance scale. 1) Seek to Isolate the variable TO ONE SIDE. 2) Cancel by doing the opposite operation. 3) Do the same thing to both sides. -1(y + 7) = - 6y + 8 -y – 7 = - 6y y = + 6y 5y - 7 = 8 +7 = +7 5y = y = (2a + 1) = 3(a-2) (2a + 1) = 9(a-2) 4a + 2 = 9a = +18 4a + 20 = 9a -4a = -4a 20 = 5a 5 4 = a Be sure to practice, practice, practice solving equations before moving on to the next video! NOW WHAT? 1 ) Re-watch/Re-wind 2) Master Practice Problems 3) Next Skill: Solutions and Checking You Work