One-Step Inequalities

Show your work for each problem.

1.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Subtract 5 from both sides: , so .
2.
Solve for : . Enter only the number.
Answer: 10
Add 7 to both sides: , so . The boundary value is 10.
3.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Divide both sides by 3: , so . Since we divided by a positive number, the sign stays the same.
4.
Solve:
Answer: 20
1. What operation is being performed on x? division
2. What is the inverse operation? multiplication
3. Multiply both sides by 4. What is ? 20
4. Does the sign flip? (yes/no) no
5.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Divide by -2 and FLIP: , so . The sign flips because we divided by a negative.
6.
Solve: . Enter only the number for the boundary.
Answer: -5
Divide by -5 and FLIP: , so . The boundary is -5.
7.
Solve:
Answer: -12
1. What is x being divided by? -3
2. Is this number positive or negative? negative
3. When we multiply by -3, does the sign flip? yes
4. What is ? -12
8.
Which of the following requires flipping the inequality sign?
1. a)
2. b)
3. c)
4. d)
Answer:
Only requires flipping because we must divide by . Adding/subtracting negative numbers (like in the other options) does NOT flip the sign.
9.
Solve the word problem: A shop requires at least 150 euros in daily sales. If each item sells for 25 euros, how many items must be sold?
Answer: 6
1. Let = number of items. What is the total sales in terms of ? 25n
2. The sales must be 'at least' 150. What symbol means 'at least'? >=
3. Write the inequality: 25n >= 150
4. Divide both sides by 25. What is the minimum ? 6
10.
Solve:
1. a)
2. b)
3. c)
4. d)
Answer:
Multiply by and FLIP: , so .
11.
Solve: . Enter only the number for the boundary.
Answer: 5
Divide by -7 and FLIP: , so . The boundary is 5.
12.
A freezer must stay below . It's currently at and drops per hour. After how many hours will it be cold enough?
Answer: 3
1. What is the starting temperature? -3
2. After hours, the temp is . It must be below . Write the inequality: -3 - 4h < -15
3. Subtract -3 from -15: what is ? -12
4. Solve . Divide by -4 and flip: 3
13.
Solve:
Answer: 8
1. What is being added to x? 12
2. What is the inverse of adding 12? subtracting 12
3. Calculate: 8
14.
Solve: . Enter only the number.
Answer: 7
Divide by 8: , so .
15.
Solve:
Answer: -12
1. To isolate x, what should we multiply by? -6
2. Is -6 positive or negative? negative
3. When multiplying by negative, do we flip? yes
4. Calculate : -12
16.
Which value is a solution to ?
1. a)
2. b)
3. c)
4. d)
Answer:
. Only is greater than 8. Note: does NOT work because we need strictly greater than.