Activating Prior Knowledge – Notes M4:LSN6 Solving Linear Equations Activating Prior Knowledge – Notes Solve the equation. 𝟏. 𝟓𝒙− 𝒙+𝟑 = 𝟏 𝟑 𝟗𝒙+𝟏𝟖 −𝟓 5𝑥−𝑥−3=3𝑥+6−5 4𝑥−3=3𝑥+1 −3𝑥 −3𝑥 𝑥−3=1 +3 +3 𝑥=4 Tie to LO

Today, we will solve linear equations. Learning Objective Today, we will solve linear equations. CFU

Concept Development Review M4:LSN4 Solving Linear Equations Concept Development Review To solve an equation means to find all of the numbers x, if they exist, so that the given equation is true. x + 2 = 3 CFU

Concept Development – Notes #1 M4:LSN6 Solving Linear Equations Concept Development – Notes #1 CFU

Use the distributive property to transform the expression. M4:LSN5 Writing and Solving Linear Equations Concept Development – Notes Use the distributive property to transform the expression. 2(x + 2) 5(2x + 2) 𝟏 𝟐 (6x + 10) -3(3x + 2) CFU

CFU Solving Linear Equations 4x + 3(4x + 7) = 4(7x + 3) - 3 M4:LSN6 Solving Linear Equations Skill Development/Guided Practice – Notes #2 4x + 3(4x + 7) = 4(7x + 3) - 3 4x + 12x + 21 = 28x + 12 - 3 16x + 21 = 28x + 9 - 16x -16x 21 = 12x + 9 - 9 -9 12 = 12x ÷12 ÷12 1 = x CFU

Concept Development Review M4:LSN4 Solving Linear Equations Concept Development Review – Pair Share What are we distributing in this problem? -(3 + x) 4(3 + x) CFU

CFU Solving Linear Equations 20 – (3x – 9) – 2 = - (-11x + 1) M4:LSN6 Solving Linear Equations Skill Development/Guided Practice – Notes #3 20 – (3x – 9) – 2 = - (-11x + 1) 20 – 1(3x – 9) – 2 = - 1(-11x + 1) 20 - 3x + 9 -2 = 11x -1 -3x + 27 = 11x - 1 + 1 +1 -3x + 28 = 11x + 3x +3x 28 = 14x ÷14 ÷14 2 = x CFU

CFU Solving Linear Equations 2x + 1 = - (5x + 9) 2x + 1 = - 1(5x + 9) M4:LSN6 Solving Linear Equations Skill Development/Guided Practice – Notes #4 2x + 1 = - (5x + 9) 2x + 1 = - 1(5x + 9) 2x + 1 = -5x - 9 + 5x +5x 7x + 1 = -9 -1 -1 7x = -10 ÷7 ÷7 x = − 𝟏𝟎 𝟕 CFU

Does an equation always have a solution? M4:LSN3 Linear Equations in x Concept Development Review – Pair Share Does an equation always have a solution? What does it mean if an equation doesn’t have a solution, like in x + 1 = x + 2? CFU

What does this say about the equation 2(x +1) = 2x – 3? M4:LSN6 Solving Linear Equations Concept Development 2(x + 1) = 2x - 3 2x + 2 = 2x - 3 - 2x -2x 2 = -3 Does 2 = -3? What does this say about the equation 2(x +1) = 2x – 3? CFU

What does this say about the equation 9(4 – 2x) – 3 = - 18x? M4:LSN6 Solving Linear Equations Skill Development/Guided Practice – Notes #5 9(4 – 2x) – 3 = - 18x 36 – 18x - 3 = - 18x + 18x +18x 36 – 3 = 0 33 = 0 Does 33 = 0? What does this say about the equation 9(4 – 2x) – 3 = - 18x? CFU

62 -10x = 6x - 6 CFU Solving Linear Equations M4:LSN6 Solving Linear Equations Skill Development/Guided Practice – Notes #6 17 – 5(2x – 9) = - (-6x + 10) + 4 17 – 5(2x – 9) = - 1(-6x + 10) + 4 17 - 10x + 45 = 6x – 10 + 4 62 -10x = 6x - 6 + 10x +10x 62 = 16x - 6 + 6 +6 68 = 16x ÷16 ÷16 𝟔𝟖 𝟏𝟔 = x 𝟏𝟕 𝟒 = x CFU

– Complete at the end of your notes Closure – Complete at the end of your notes 1. What did we learn today? 2. Why is this important to you? 3. How can you tell if a value of x is a solution to an equation? Homework: Problem Set page 19 problems 1 – 7 all You MUST complete the homework on a separate sheet of paper to receive credit! CFU