Solving Multi-Step Equations

Show your work for each problem.

1.
What is the first step to solve ?
1. a)Divide both sides by 2
2. b)Multiply both sides by 2
3. c)Subtract 5 from both sides
4. d)Add 5 to both sides
Answer: Subtract 5 from both sides
We undo operations in reverse order. Since was added to , we first subtract from both sides to get , then divide by .
2.
Solve:
Answer: 5
→ → → . Check: ✓
3.
What is when expanded using the distributive property?
1. a)
2. b)
3. c)
4. d)
Answer:
. Each term inside must be multiplied by .
4.
Solve:
Answer: 4
1. What should you subtract from both sides first? 3
2. After subtracting, what is equal to? 16
3. Divide by 4. What is ? 4
5.
Solve:
Answer: 7
→ → . Check: ✓
6.
Solve:
Answer: 4
1. Apply the distributive property. What is ? 2x + 6
2. Now subtract 6 from both sides. What is ? 8
3. Divide both sides by 2. What is ? 4
7.
Solve:
Answer: 4
→ → → →
8.
When combining like terms in , what is the simplified expression?
1. a)
2. b)
3. c)
4. d)
Answer:
. The stays separate because it has no variable.
9.
Solve:
Answer: 4
1. Subtract from both sides. What do you get on the left? 4x - 4
2. Add 4 to both sides. What is equal to? 16
3. Divide by 4. What is ? 4
10.
Solve:
Answer: 7
→ → → . Check: ✓
11.
Solve:
Answer: 5
1. Combine like terms: 3x
2. So the equation becomes . What is ? 15
3. What is ? 5
12.
Solve:
Answer: 3
→ → → →
13.
Solve:
Answer: 4
1. Distribute 2 on the left. What do you get? 6x - 2
2. Subtract from both sides. What's on the left? 2x - 2
3. Add 2 to both sides. What is ? 8
4. What is ? 4
14.
Which equation has the solution ?
1. a)
2. b)
3. c)
4. d)
Answer:
Substituting : ✓. The other options give different results when .
15.
Solve:
Answer: 3
1. Distribute 3 in . What do you get? 6x + 3
2. Simplify the left side: 6x - 1
3. Subtract from both sides. What is on the left? x - 1
4. Add 1 to both sides. What is ? 3
16.
Solve:
Answer: 5
→ → → . Check: and ✓