 # Solving Two-Step Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations?

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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?

EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x 2 11 + 5 – 5 = x 2 11 – 5 Subtraction Property of Equality = x 2 6 Simplify. 2 = 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.

EXAMPLE 1 Solve a two-step equation CHECK + 5 = x 2 11 Write original equation. 11 + 5 = 12 2 ? Substitute 12 for x. Simplify. Solution checks. 11 = 11 

GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 1. 5x + 9 = 24 SOLUTION 5x + 9 = 24 Write original equation. 5x + 9 – 9 = 24 – 9 Subtraction Property of Equality 5x = 15 Simplify. 5x5x 5 = 15 5 Division Property of Equality x = 3 Simplify.

GUIDED PRACTICE for Example 1 CHECK Simplify. Solution check. Substitute 3 for x. ANSWER The solution is 3. Check by substituting 3 for x in the original equation. 5x + 9 = 24 Write original equation. 24 5 3 + 9 = ? 24 = 24

GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 2. 4y – 4 = 16 SOLUTION 4y – 4 = 16 Write original equation. 4y – 4 + 4 = 16 + 4 Addition Property of Equality 4y = 20 Simplify. 4y4y 4 20 4 = Division Property of Equality. y =5 Simplify.

GUIDED PRACTICE for Example 1 ANSWER The solution is 5. Check by substituting 5 for y in the original equation. CHECK Simplify. Solution checks. Substitute 5 for y. 4y – 4 = 16 Write original equation. 16 4(5) – 4 = ? 16 = 16

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

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

Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide each side by 3. x = 7 Simplify. = 3 3x3x 3 21

GUIDED PRACTICE for Examples 2 and 3 8t – 3t = 35 Write original equation. 5t = 35 Substract the like terms Divide each side by 5 t = 7 Simplify. 5 = 5t5t 5 35 5. 8t – 3t = 35 Solve the equation. Check your solution.

GUIDED PRACTICE for Examples 2 and 3 CHECK 8t – 3t = 35 Write original equation. Multiply. 35 =35 8(7) – 3(7) = 35 ? Substitute 7 for t. 56 – 21 = 35 ? Simplify. Solution checks.

GUIDED PRACTICE for Example 4 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? Jobs Write the equation 53–13 = 13 –13 + 8h 53 = 13 + 8h 40 = 8h Simplify. Subtraction Property of Equality. SOLUTION 5 = h Division Property of Equality

GUIDED PRACTICE for Example 4 ANSWER She worked for 5 hours

Essential Question: How do you solve two-step equations?

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