1. Solve an equation by combining like terms
EXAMPLE 1
Solve an equation by combining like terms
Solve
8x – 3x – 10 = 20
8x – 3x – 10 = 20
Write original equation.
5x – 10 = 20
Combine like terms.
5x – =
Add 10 to each side.
5x = 30
Simplify. = 30 5 5x
Divide each side by 5.
x = 6
Simplify.

2. EXAMPLE 2
Solve an equation using the distributive property
Solve
7x + 2(x + 6) = 39.
SOLUTION
When solving an equation, you may feel comfortable doing some steps mentally. Method 2 shows a solution where some steps are done mentally.

3. EXAMPLE 2
METHOD 1
METHOD 2
Do Some Steps Mentally
Show All Steps
7x + 2(x + 6) = 39
7x + 2(x + 6) = 39
7x + 2x + 12 = 39
7x + 2x + 12 = 39
9x + 12 = 39
9x + 12 = 39
9x + 12 – 12 = 39 – 12
9x = 27
9x = 27
x = 3 = 9x 9 27
x = 3

4. EXAMPLE 3
Standardized Test Practice
SOLUTION
In Step 2, the distributive property is used to simplify the left side of the equation. Because – 4(x – 3) = – 4x+ 12,
Step 2 should be 5x – 4x + 12 = 17.
ANSWER
The correct answer is D. A C D B

5. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
9d – 2d + 4 = 32 1.
9d – 2d + 4 = 32
Write original equation.
7d + 4 = 32
Combine like terms.
7d + 4 – 4 = 32 – 4
Subtract 4 from each side.
7d = 28
Simplify = 28 7 7d
Divide each side by 5.
d = 4
Simplify.

6. GUIDED PRACTICE for Examples 1, 2, and 3 Check 9d – 2d + 4 = 32
Write original equation.
9(4) – 2(4) + 4 = 32 ?
Substitute 4 for d.
36 – = 32 ?
Multiply.
32 = 32
Simplify. Solution checks.

7. EXAMPLE 2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
2w + 3(w + 4) = 27 2.
2w + 3(w + 4) = 27
2w + 3w + 12 = 27
5w + 12 = 27
5w + 12 – 12 = 27 – 12
5w = 15 = 5w 5 15
w = 3

8. GUIDED PRACTICE for Examples 1, 2, and 3 Check 2w + 3(w +4) = 27
Write original equation.
2(3) + 3(3 + 4) = 27 ?
Substitute 3 for w.
6 + 3(7) = 27 ?
Simplify.
= 27 ?
Multiply.
27 = 27
Simplify solution checks.

9. EXAMPLE 2
GUIDED PRACTICE
for Examples 1, 2, and 3
Solve the equation. Check your solution.
6x – 2(x – 5) = 46 3.
6x – 2(x – 5) = 46
6x – 2x + 10 = 46
4x + 10 = 46
4x + 10 – 10 = 46 – 10
4x = 36 = 4x 4 36
x = 9

10. GUIDED PRACTICE for Examples1, 2, and 3 Check 6x – 2(x – 5) = 46
6(9) – 2(9 – 5) = 46 ?
54 – 2(4) = 46 ?
54 – 8 = 46 ?
46 = 46