Solving Inequalities
Expressions
Word Problems
100
Solve the inequality, 2(6 − x) ≤ 4x. Then graph on a number line.
2≤x
100
Simplify 2(a+3)+4(a−1).
6a+2
100
If a number is multiplied by 3 and then decreased by 5, the result is 10. What is the number?
5
200
A theme park has a height requirement for a ride: riders must be at least 54 inches tall. If Jenna is currently hhh inches tall, what is the inequality that represents how tall she needs to be to ride?
Inequality: h≥54
200
Simplify 2(a+3)+4.
Answer: 2a+10
200
A rectangle has a length that is twice its width. If the perimeter is 36, what are the dimensions?
Width = 6, Length = 12
300
A concert venue can hold at most 500 people. If 120 tickets have already been sold, how many more tickets can be sold without exceeding the venue's capacity? Write and solve the inequality.
Inequality: 120+x≤500
Solution: x≤380
300
Simplify 4(2x+3)−5(x−1).
3x+22
300
A house-painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount?
x=32
400
A cargo plane can carry a maximum weight of 10,000 pounds. If a shipment weighs 2,500 pounds, how much more weight can be added without exceeding the limit? Write and solve the inequality.
Inequality: 2500+x≤10000
x≤7500
400
Solve for X. Then label if it has one, no, or many solutions.
3(2x – 1) + 5 = 6(x+1)
No solution.
400
An equilateral triangle has side lengths of 3x while a square has side lengths of x+5. If the two figures have the same perimeter, what is the side length of the square?
9
500
John has $28 and is saving $13 per month. Tim has $52 and is saving $7 per month. When will John have more money saved than Tim?
28 + 13m > 52 + 7m
m > 4
John will have more money than Tim after more than 4 months.
500
Solve for X. Then label if it has one, no, or many solutions.
6 – 2x – 1= 4x + 8 – 6x – 3
All real
numbers
500
Lucia is going skating. Skate Country charges $5 for admission plus $2 per hour for skate rental. Skate Along charges $10 for admission plus $1 per hour for skate rental. How long can Lucia skate so that Skate Country is cheaper?
5 + 2h < 10 + h
h < 5
If Lucia skates between 0 and 5 hours, Skate Country will be cheaper than Skate Along.