Two-Step Inequalities

Show your work for each problem.

1.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 3: . Divide by 2: . No flip needed since 2 is positive.
2.
Solve: . What is the boundary value for ?
Answer: 7
Add 6: . Divide by 3: . The boundary value is 7.
3.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 4: . Multiply by 2: .
4.
Solve:
Answer: 3
1. What do we subtract from both sides first? 8
2. After subtracting 8, we have ? 12
3. Divide both sides by 4. What is ? 3
4. Is the sign flipped? (yes/no) no
5.
Solve: . What is the boundary value?
Answer: 7
Add 10: . Divide by 5: . The boundary is 7.
6.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 6: . Divide by -2 and FLIP: .
7.
Solve:
Answer: -3
1. Subtract 9 from both sides. What is ? 9
2. We need to divide by -3. Will the sign flip? (yes/no) yes
3. After dividing by -3 and flipping, is... (>= or <=)? >=
4. What is ? -3
8.
Solve: . What is the boundary value for ?
Answer: -4
Subtract 7: . Divide by -2 and flip: . The boundary is -4.
9.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 5: . Multiply by -3 and flip: .
10.
Solve:
Answer: -3
1. Subtract 8 from both sides. What is ? 15
2. We divide by -5. Does the sign flip? (yes/no) yes
3. What is ? -3
4. The final answer is ... (< / > / <= / >=) -3 <=
11.
Solve: . What is the boundary value?
Answer: -5
Add 8: . Divide by -4 and flip: . The boundary is -5.
12.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by 3: . Subtract 4: . Divide by 2: .
13.
Solve:
Answer: -1
1. Multiply both sides by -2. Does the sign flip? (yes/no) yes
2. After multiplying by -2 and flipping, ... (>= or <=)? >=
3. What is ? -12
4. Now solve . Add 9: ? -3
5. Divide by 3: ? -1
14.
Solve: . What is the boundary value?
Answer: 3
Subtract 15: . Divide by -6 and flip: . The boundary is 3.
15.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 5: . Divide by -7 and flip: , or .
16.
A phone plan costs 20 euros per month plus 0.05 euros per text. If you can spend at most 35 euros, how many texts can you send?
Answer: 300
1. What is the fixed monthly cost? 20
2. If you send texts, the variable cost is... 0.05t
3. The inequality is . Subtract 20: ? 15
4. Divide by 0.05: ? 300
17.
You have 200 euros saved. Each week you spend 15 euros. You want to keep at least 50 euros. For how many weeks can you do this?
Answer: 10
. Subtract 200: . Divide by -15 and flip: . You can do this for 10 weeks.
18.
A freezer starts at 8°C and cools by 4°C per minute. It needs to reach at most -12°C. After how many minutes?
Answer: 5
1. After minutes, the temperature is . We need this to be at most -12. What inequality symbol? (< / <= / > / >=) <=
2. Subtract 8 from both sides: ? -20
3. Divide by -4. Does the sign flip? (yes/no) yes
4. After flipping, ... (< / <= / > / >=)? >=
5. What is ? 5