One-Step
One-Step Inequalities Guide
Learn inequality symbols, inverse operations, solution graphs, and the rule for multiplying or dividing by a negative number.
Read the One-Step GuideFree Interactive Algebra Tool
Step-by-Step Solving Inequalities Practice
Practice one-step, two-step, and multi-step inequalities while showing each algebra step. Learn when the inequality symbol stays the same and when multiplying or dividing by a negative reverses it.
Start practicingLearn Before You Practice
Choose the Inequalities Guide You Need
Review the level that matches what you are practicing, or work through all three guides as your inequality skills progress.
Two-Step
Two-Step Inequalities Guide
Undo constants and coefficients in order while keeping track of whether the inequality symbol must reverse.
Read the Two-Step Guide
Multi-Step
Multi-Step Inequalities Guide
Practice distribution, combining like terms, negative values, and longer inequality solution chains.
Read the Multi-Step Guide
Problem 1 of 10
10%
Current equation
Simplify the equation before isolating the variable.
Original equation
3x + 5 < 20
Your work
0 steps completed
- Start 3x + 5 < 20
Solve this equation
3x + 5 < 20
Final Step
Graph the solution
Show the solution set on the number line. Select the boundary point, decide whether the endpoint is open or closed, and choose the direction of the solution.
Your solution
x < 5
Selected boundary:
None yet
Is the boundary included?
Which direction contains the solutions?
Use inverse operations to isolate the variable. If you multiply or divide by a negative number, reverse the inequality symbol.
Hint
Look for parentheses or like terms first. Simplify the equation before using inverse operations.
Inequality reference
Adding or subtracting the same value does not reverse the inequality.
Multiplying or dividing by a positive number keeps the symbol the same.
Reverse the inequality symbol whenever you multiply or divide both sides by a negative number.
Remove the constant first, then undo the coefficient.
Distribute and combine like terms before using inverse operations.
The solution is a range of values, not usually a single number.
Problems Solved
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Correct Steps
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Incorrect Attempts
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Practice Round Complete
Great work!
You completed all 10 inequality problems.
Problems Solved
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Keep the inequality balanced
Apply the same operation to both sides while working toward an isolated variable.
Know when to reverse the sign
Multiplying or dividing both sides by a negative number reverses the inequality symbol.
Practice every level in one tool
Move from one-step inequalities through two-step, multi-step, and mixed review.
Important Rule
When does the inequality symbol reverse?
It reverses only when both sides are multiplied or divided by a negative number.
−2x < 8
1
Divide both sides by −2
−2x ÷ (−2) ? 8 ÷ (−2)
2
Reverse the inequality symbol
x > −4
The symbol changes from < to > because the inequality was divided by a negative number.
Practice Solving One-Step, Two-Step, and Multi-Step Inequalities
Inequalities use many of the same inverse-operation skills as equations, but the solution usually represents a range of values instead of one number.
This tool combines one-step, two-step, and multi-step inequality practice in one place. Students rewrite the complete inequality after each valid step so the changing algebra remains visible.
One-Step Inequalities
Begin with a single inverse operation and learn the special rule for multiplying or dividing by negative numbers.
Two-Step Inequalities
Remove the constant first, then undo the coefficient or divisor while checking whether the inequality symbol must reverse.
Multi-Step Inequalities
More advanced problems may require distribution, combining like terms, simplifying constants, and several inverse operations.
Why Does the Inequality Sign Flip?
Multiplying or dividing an inequality by a negative number reverses the order of the values. For example, dividing −2x < 8 by −2 gives x > −4.
Mixed Inequality Review
Mixed Review combines all three levels so students must recognize the structure of the inequality before deciding what algebra step comes next.
Free Inequality Practice on Any Device
Use the tool on a desktop computer, tablet, or phone for tutoring sessions, homework support, classroom review, or independent algebra practice.