7th Grade Inequalities- Word Problems Worksheet and Solutions

What You'll Find Here

This page has practice worksheets with real 7th grade inequalities word problems and complete solutions. No fluff. Just problems you can actually use.

Quick Review: What Are Inequalities?

An inequality shows when things aren't equal. Instead of an equals sign, you get:

> greater than
< less than
≥ greater than or equal to
≤ less than or equal to

The solution to an inequality is usually a range of numbers, not just one answer. That's where most students get stuck.

How to Solve Word Problems

Here's the process that actually works:

Read the problem twice. The first read is to understand. The second is to extract numbers.
Identify the variable. Figure out what you're solving for and call it x.
Build the inequality. Translate the words into math symbols.
Solve it. Use reverse order of operations.
Check your answer. Plug it back into the original problem.

Translation Guide

Words	Math Symbol
at most, no more than, maximum	≤
at least, minimum, no less than	≥
exceeds, more than, greater than	>
fewer than, less than, under	<

Worksheet: Practice Problems

Solve each problem. Show your work. Answers are below.

Problem 1

Maya wants to buy a skateboard that costs $85. She already has $23. She earns $12 per week allowance. How many weeks does she need to save to have at least $85?

Problem 2

A taxi charges $3.50 base fare plus $2.30 per mile. Marcus has $20. How many miles can he travel if he doesn't want to run out of money?

Problem 3

Jordan needs a 92 average to get an A in math. His first three test scores are 88, 95, and 91. What score does he need on the fourth test to earn an A?

Problem 4

A fitness center charges $45 per month for membership. They also require a one-time $120 enrollment fee. How many months can someone subscribe if they want to spend no more than $600 total?

Problem 5

Tickets to a concert cost $28 each. If you buy more than 5 tickets, you get $4 off per ticket. A group has $350 to spend. What's the maximum number of tickets they can buy?

Problem 6

A rectangle's length is 3 times its width. The perimeter must be less than 48 inches. What are the possible widths?

Problem 7

Sophia sells homemade candles. She spends $8 on materials per candle. She wants to charge at least $20 per candle to make a profit. She has $200 budgeted for production. How many candles can she make while maintaining her minimum price?

Problem 8

A phone plan costs $15 per month plus $0.08 per text message. If someone wants to keep their bill under $25, what's the maximum number of texts they can send?

Solutions

Problem 1 Solution

Setup: $23 + 12w ≥ 85

Subtract 23 from both sides: 12w ≥ 62

Divide by 12: w ≥ 5.17

Answer: Maya needs at least 6 weeks (you can't have partial weeks in this context).

Problem 2 Solution

Setup: 3.50 + 2.30m ≤ 20

Subtract 3.50: 2.30m ≤ 16.50

Divide by 2.30: m ≤ 7.17

Answer: Marcus can travel at most 7 miles.

Problem 3 Solution

Setup: (88 + 95 + 91 + x) / 4 ≥ 92

Add scores: 274 + x ≥ 368

Subtract 274: x ≥ 94

Answer: Jordan needs at least 94 on his fourth test.

Problem 4 Solution

Setup: 45m + 120 ≤ 600

Subtract 120: 45m ≤ 480

Divide by 45: m ≤ 10.67

Answer: They can subscribe for at most 10 full months.

Problem 5 Solution

Setup: Since the discount applies when buying more than 5 tickets, test that scenario first.

Discounted price: $28 - $4 = $24 per ticket

Inequality: 24t ≤ 350

t ≤ 14.58

Answer: Maximum 14 tickets.

Problem 6 Solution

Setup: Length = 3w

Perimeter formula: 2(length + width) < 48

2(3w + w) < 48

2(4w) < 48

8w < 48

Answer: Width must be less than 6 inches (w < 6).

Problem 7 Solution

Setup: 8c ≤ 200 (cost constraint)

c ≤ 25

Answer: Sophia can make at most 25 candles.

Problem 8 Solution

Setup: 15 + 0.08t < 25

Subtract 15: 0.08t < 10

Divide by 0.08: t < 125

Answer: Maximum 124 text messages.

Where Students Go Wrong

Flipping the sign when multiplying or dividing by a negative number. Always check this.
Forgetting to check if the problem asks for whole numbers (weeks, tickets, months). You can't buy 5.17 weeks of allowance.
Using the wrong inequality symbol. "At most" means ≤. "At least" means ≥.
Not testing the boundary. If your answer is x ≥ 5, test x = 5 in the original problem.

Using These Worksheets in Class

Assign problems 1-4 as homework. Save 5-8 for assessment or extra practice. The difficulty ramps up, so don't assign them all at once unless your students are solid on basics.