Solving Two-StepSolving Two-StepEquationsEquations

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

Whatever you do to one side, you must Whatever you do to one side, you must do to the other side to keep property do to the other side to keep property of equality.of equality.

Steps for Solving Two-Step Equations

1.Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation.

2.Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

Inverse Operations Addition SubtractionMultiplication Division

Example 1: Solve 4x – 5 = 15

4x – 5 = 15 +5 +5 (Add 5 to both sides)4x = 20(Simplify) 4 4 (Divide both sides by 4)x = 5 (Simplify)Check:

4(5) -5 =15 20 – 5 = 15 15 =15

EXAMPLE 2 Solve a two-step equation

Solve + 5 = 11.x2

Write original equation.+ 5 = x2

11

+ 5 – 5 = x2 11 – 5 Subtraction Property of Equality

= x2

6 Simplify.

2 =x2 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 2 Solve a two-step equation

CHECK + 5 = x2

11 Write original equation.

11+ 5 = 122

?Substitute 12 for x.

Simplify. Solution checks.11 = 11

GUIDED PRACTICE for Example 1 &2

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.

5x5 = 15

5Division 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.

245 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.

4y4

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.

164(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 = –7z3

– 1 = z3 – 7

– 1 + 7 = z3 – 7 + 7

6 = z3

6 =3 z33

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 = z3 – 7

183 – 7– 1 =

?

– 1 = – 1

Solve a two-step equation by combining like terms

EXAMPLE 3

Solve 7x – 4x = 21

7x – 4x = 21 Write original equation.

3x = 21 Combine like terms.

Divide each side by 3.

x = 7 Simplify.

= 33x

321

GUIDED PRACTICE for Examples 3

8t – 3t = 35 Write original equation.

5t = 35 Substract the like terms

Divide each side by 5

t = 7 Simplify.

5 =5t 535

5. 8t – 3t = 35

Solve the equation. Check your solution.

GUIDED PRACTICE for Examples 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: Essential Question:

How do you solve two-step equations?