Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Every time you multiply or divide by a negative number, stop and reverse the inequality sign. Finish each solution by testing one number from the shaded ray in the original inequality.
Standards: 7.EE.B.4b · Level: Grade 7
Problem 2 Subtract, Then Divide ★★★
Solve 2x − 7 < 9.
Problem 3 Graph a Simple Inequality ★★★
Graph x < 3 on the number line.
Problem 4 A Quotient Inequality ★★★
Solve x5 + 2 > 6.
Problem 5 First Negative Coefficient ★★★
Solve −2x + 3 > 11 and graph the solution.
Problem 6 Negative Coefficient with Subtraction ★★★
Solve −5x − 10 < 20.
Problem 7 Decimal Coefficient ★★★
Solve 0.5x − 2.5 < 3.
Problem 8 Decimals on Both Sides of the Sign ★★★
Solve 1.2x + 3.6 > 9.6.
Problem 9 Fraction Coefficient ★★★
Find every value of x that makes 56x + 3 > 13 true, and test one value from your answer.
Problem 10 Negative Quotient ★★★
Solve −x4 + 1 > 3.
Problem 11 Parentheses and a Positive Factor ★★★
Solve 3(x − 2) > 12.
Problem 12 From Graph to Inequality ★★★
The graph shows the solution set of an inequality. Write the inequality, then show that 2x + 5 < 3 has this solution set.
Problem 13 Negative Factor Outside ★★★
Solve −2(x + 3) < 10.
Problem 14 Variable on the Right Side ★★★
Solve 18 > 7 − 2.5x.
Problem 15 Club Fundraiser Goal ★★★
A club has $60 and earns $8 profit on each T-shirt sold. It wants more than $240. Write and solve an inequality for the number of shirts n, then state the least whole number of shirts.
Problem 16 Texting Plan Budget ★★★
A phone plan costs $20 per month plus $0.05 per text. Maria wants her bill to be less than $35. Write and solve an inequality for the number of texts t.
Problem 17 Diver Ascent ★★★
A diver at −12 feet rises 4 feet each minute. After m minutes the diver must be shallower than −2 feet, meaning higher than −2. Write and solve an inequality, and graph the solution.
Problem 18 Bus Rental Budget ★★★
A school bus rental costs $150 plus $2.25 per mile. The trip budget is under $375. Write and solve an inequality for the number of miles m, and interpret the answer.
Problem 19 Draining the Pool ★★★
A pool holds 600 gallons and drains 15 gallons each minute. For how many minutes t will the pool hold fewer than 270 gallons? Write and solve an inequality, and graph the solution.
Problem 20 Markers with Tax ★★★
Mr. Ortiz buys 4 packs of markers. Each pack costs m dollars plus $1.25 in tax, and he has $30. Write an inequality for the total cost being less than $30, solve it, and describe the possible prices.
