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§ Algebra·Grade 7

Inequalities Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable inequalities worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from one-step inequality, x + b ⋚ c at the easy level through to negative coefficient requires flip at the advanced level.

CCSS.7.EECCSS.HSA.REI

What is inequalities?

An inequality compares two expressions using symbols like <, >, ≤, or ≥ instead of an equals sign. Solving inequalities follows the same steps as solving equations, with one crucial exception: multiplying or dividing both sides by a negative number flips the inequality sign. For example, -2x > 6 becomes x < -3 after dividing by -2.

Why it matters

Inequalities model countless real-world constraints and comparisons. A business needs revenue > $50,000 to break even, or a bridge must support weight ≤ 80 tons. Manufacturing requires temperatures between 150°F and 200°F, expressed as 150 ≤ T ≤ 200. Sports statistics use inequalities to define qualifying standards, like a runner needing a time < 12.5 seconds. Budget planning involves inequalities: total expenses < available funds. In advanced mathematics, inequalities define domains of functions, optimization problems in calculus, and solution regions in linear programming. The CCSS 7.EE standards emphasize solving one- and two-step inequalities, building foundations for algebra concepts in high school where inequalities appear in systems, absolute value problems, and rational functions.

Common mistakes to watch for

  • ✗When dividing -3x < 15 by -3, writing x < -5 instead of x > -5, forgetting to flip the inequality sign when dividing by a negative number.
  • ✗Solving 2x + 4 ≥ 10 and writing x ≥ 7 instead of x ≥ 3, making arithmetic errors during the isolation process.
  • ✗Graphing x > 5 with a closed circle instead of an open circle, confusing the symbols > and ≥ on number lines.

Questions teachers ask

When do you flip the inequality sign?+
The inequality sign flips only when multiplying or dividing both sides by a negative number. For example, dividing -2x > 8 by -2 gives x < -4. Adding, subtracting, or working with positive numbers never changes the inequality direction.
What's the difference between < and ≤?+
The symbol < means "less than" and excludes the boundary value, while ≤ means "less than or equal to" and includes it. For x < 5, the value 5 doesn't satisfy the inequality, but for x ≤ 5, the value 5 does satisfy it.
How do you check if your inequality solution is correct?+
Pick a test value that satisfies your solution and substitute it into the original inequality. For x > 3, try x = 4. If the original inequality becomes a true statement, your solution is correct. Test values near the boundary for best verification.
Why use open vs closed circles on number lines?+
Open circles represent < or > symbols, showing the boundary point isn't included in the solution. Closed circles represent ≤ or ≥ symbols, showing the boundary point is included. This visual distinction clarifies whether endpoint values satisfy the inequality.
Can inequalities have no solution or infinite solutions?+
Yes. The inequality x + 3 < x results in 3 < 0, which is false, so no solution exists. The inequality 2x + 4 > 2x - 1 simplifies to 4 > -1, which is always true, giving infinitely many solutions.
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Beginner

Generate →
Concepts
One-step inequality, x + b ⋚ c
Range
b: 1–5, bound: 6–15
Steps
3 steps
Example
x + 3 < 10

Easy

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Concepts
Two-step inequality, positive coeff
Range
a: 2–5, b: 1–10
Steps
4 steps
Example
3x + 4 ≤ 16

Medium

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Concepts
Two-step inequality, negative constants allowed
Range
a: 2–8, b: −10 to 10
Steps
4 steps
Example
5x − 7 > 13

Hard

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Concepts
Negative coefficient requires flip
Range
a: −5 to 8 (incl. neg), b: −15 to 15
Steps
4 steps
Example
−3x + 5 ≥ 14

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