1. 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

2. 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.

3. 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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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

16. GUIDED PRACTICE
for Example 4
ANSWER
She worked for 5 hours

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