1.1 Solving Equations. Today’s Learning Targets I will be abe to apply inverse opertions to isolate a variable solve multi-step equations in an algebraic.

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Presentation transcript:

1.1 Solving Equations

Today’s Learning Targets I will be abe to apply inverse opertions to isolate a variable solve multi-step equations in an algebraic proof solve application problems using inverses

Open Sentence: A mathematical statement that contains algebraic expressions and a symbol that compares them

Guess and check method: Is 5 a solution? 24 – 3d = 9 3x + 4 = 18 2w – 7 < w > 19

Equation  An open sentence that contains the symbol =.

Solve equations using inverse operations to produce equivalent equations. What are inverse operations? What are equivalent equations?

Properties of Equality Addition Property of Equality Add the same number to both sides of the equation to produce an equivalent equation. Subtraction Property of Equality Subtract the same number from both sides of the equation to produce an equivalent equation.

Properties of Equality Multiplication Property of Equality Multiply both sides of the equation by the same nonzero number to produce an equivalent equation. Division Property of Equality Divide each side of the equation by the same nonzero number to produce an equivalent equation.

How to show your work… 1.Write the original equation. 2.Use properties of equality to solve the problem 3.Check your work.

Examples:

Now, write reasons for each step… Example: Solve 7(5 – x ) = 14 EquationExplanationReason 7(5 – x ) = 14Write original equation Given 35 – 7x = 14MultiplyDistributive property -7x = -21Subtract 35 from each side Subtraction property of equality x = 3Divide each side by -7 Division property of equality

Your turn, Example: Solve 5(x – 2) = 4 EquationExplanationReason

Your turn, Example: Solve 5(x – 2) = 4 EquationExplanationReason 5(x–2) =4Write original equation Given

Your turn, Example: Solve 5(x – 2) = 4 EquationExplanationReason 5(x–2) =4Write original equation Given 5x-10 =4MultiplyDistributive property

Your turn, Example: Solve 5(x – 2) = 4 EquationExplanationReason 5(x–2) =4Write original equation Given 5x – 10 =4MultiplyDistributive property 5x = 14Add 10 to both sides Addition property of equality

Your turn, Example: Solve 5(x – 2) = 4 EquationExplanationReason 5(x–2) =4Write original equation Given 5x -10 =4MultiplyDistributive property 5x = 14Add to 10 both sides Addition property of equality x = 2.8Divide both sides by 5 Division property of equality

Polya’s 4 step method: 1. Identify the unknown and write a let statement 2. Write an equation for the situation 3. Solve the equation 4. Answer the question using units

Farmer’s Market To rent a booth at the farmer’s market costs $20 per week plus a one-time equipment fee of $85. Find the number of weeks Mr. Vegetable rented a booth if he paid a total of $325.

Function Junction The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is -6.

Money, Money A bank charges $5.00 per month plus $0.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month.

Assignment for 1.1 Due Tuesday Page 9 # 4 – 14 even, 15 – 22 all (skip 19), 24 – 26