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**Solving Two-Step Equations**

You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations? TP: Construct and solve two step equations for real world problems by combining like terms

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**Addition Subtraction Multiplication Division**

Steps for Solving Two-Step Equations Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation. Inverse Operations Addition Subtraction Multiplication Division Whatever you do to one side, you must do to the other side to keep property of equality.

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Example 1: Solve 4x – 5 = 15 4x – 5 = 15 (Add 5 to both sides) 4x = 20 (Simplify) (Divide both sides by 4) x = 5 (Simplify) Check: 4(5) -5 =15 20 – 5 = 15 15 =15

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**Solve a two-step equation**

EXAMPLE 2 Solve a two-step equation Solve = 11. x 2 + 5 = x 2 11 Write original equation. + 5 – 5 = x 2 11 – 5 Subtraction Property of Equality = x 2 6 Simplify. = x 2 2 6 Multiplication Property of Equality. x = 12 Simplify. ANSWER The solution is 12. Check by substituting 12 for x in the original equation.

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**Solve a two-step equation**

EXAMPLE 2 Solve a two-step equation + 5 = x 2 11 CHECK Write original equation. 11 + 5 = 12 2 ? Substitute 12 for x. 11 = 11 Simplify. Solution checks.

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**Solve the equation. Check your solution. 1. 5x + 9 = 24**

GUIDED PRACTICE for Example 1 &2 Solve the equation. Check your solution. x + 9 = 24 SOLUTION 5x + 9 = 24 Write original equation. 5x + 9 – 9 = 24 – 9 Subtraction Property of Equality 5x = 15 Simplify. 5x 5 = 15 Division Property of Equality x = 3 Simplify.

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**GUIDED PRACTICE for Example 1 ANSWER**

The solution is 3. Check by substituting 3 for x in the original equation. CHECK 5x + 9 = 24 Write original equation. 24 = ? Substitute 3 for x. 24 = 24 Simplify. Solution check.

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**Solve the equation. Check your solution. 2. 4y – 4 = 16**

GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. y – 4 = 16 SOLUTION 4y – 4 = 16 Write original equation. 4y – = 16 + 4 Addition Property of Equality 4y = 20 Simplify. 4y 4 20 = Division Property of Equality. y = 5 Simplify.

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**GUIDED PRACTICE for Example 1 ANSWER**

The solution is 5. Check by substituting 5 for y in the original equation. CHECK 4y – 4 = 16 Write original equation. 16 4(5) – 4 = ? Substitute 5 for y. 16 = 16 Simplify. Solution checks.

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**Solve the equation. Check your solution. 3. – 1 = –7 z 3 SOLUTION**

GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 3. – 1 = –7 z 3 SOLUTION – 1 = z 3 – 7 Write original equation. – = z 3 – 7 + 7 Add 7 to each side. 6 = z 3 Simplify. 6 = 3 z Multiply each side by 3. 18 = z Simplify.

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**GUIDED PRACTICE for Example 1 ANSWER**

The solution is 18. Check by substituting 18 for z in the original equation. – 1 = z 3 – 7 CHECK Write original equation. 18 3 – 7 – 1 = ? Substitute 18 for z. – 1 = – 1 Simplify. Solution checks.

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**Solve a two-step equation by combining like terms**

EXAMPLE 3 Solve a two-step equation by combining like terms Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. = 3 3x 21 Divide each side by 3. x = 7 Simplify.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 Solve the equation. Check your solution. t – 3t = 35 8t – 3t = 35 Write original equation. 5t = 35 Substract the like terms 5 = 5t 35 Divide each side by 5 t = 7 Simplify.

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**GUIDED PRACTICE for Examples 3 CHECK 8t – 3t = 35 ? 8(7) – 3(7) = 35 ?**

Write original equation. 8(7) – 3(7) = 35 ? Substitute 7 for t. 56 – 21 = 35 ? Multiply. 35 =35 Simplify. Solution checks.

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**GUIDED PRACTICE for Example 4 Jobs**

10. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work? SOLUTION 53 = h Write the equation 53–13 = 13 –13 + 8h Subtraction Property of Equality. 40 = 8h Simplify. 5 = h Division Property of Equality

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GUIDED PRACTICE for Example 4 ANSWER She worked for 5 hours

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**How do you solve two-step equations?**

Essential Question:

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