Inequality Solver

How to use Inequality Solver

What you can do with Inequality Solver

Solve and graph inequalities. Here are some of the most popular ways students use Inequality Solver every day:

• Breaks every problem into clear, logical steps
• Covers KS1 through A-Level — grows with your child
• Available any time, 100% free, no limits
• Ask unlimited follow-up questions — the AI never loses patience or gives up on you
• Works alongside any textbook, worksheet, or school resource

Inequalities are woven throughout GCSE algebra and A-Level mathematics, yet many UK students approach them with less confidence than equations. The key difference—and the source of most mistakes—is that multiplying or dividing by a negative number flips the inequality sign, a rule many students rush through or forget. Our Inequality Solver takes the anxiety out of solving and graphing inequalities, showing you step-by-step how to manipulate the expression, when to flip the sign, and how to represent the solution on a number line or coordinate plane. From simple linear inequalities to complex compound inequalities and two-variable inequalities defining regions, Applaa's solver builds your intuition and prevents careless errors. Free and designed for GCSE and A-Level students, the tool works offline and adjusts difficulty automatically as you progress.

How to solve and graph inequalities correctly

Solving an inequality is almost identical to solving an equation—perform the same operations on both sides to isolate the variable. The critical difference: whenever you multiply or divide both sides by a negative number, flip the inequality sign. For example, to solve -3x > 12, divide both sides by -3 and flip: x < -4. Once you have the solution, represent it on a number line using an open circle (< or >) or a closed circle (≤ or ≥). For two-variable inequalities like 2x + y < 5, rearrange to get the boundary line (2x + y = 5), then test a point to determine which side of the line satisfies the inequality. Shade that region on a coordinate grid. The Inequality Solver visualises all these steps, so you see exactly why each transformation works.

• Treat inequalities like equations until you multiply/divide by a negative number
• Remember: multiplying or dividing by a negative flips the sign (< becomes >, ≤ becomes ≥)
• On a number line: open circle for < or >, closed circle for ≤ or ≥
• For two-variable inequalities, find the boundary line first, then test a point (like (0,0)) to determine which side to shade
• Compound inequalities (e.g. -2 < x ≤ 5) are solved step-by-step: isolate x between the bounds
• Always verify: substitute your solution back into the original inequality to confirm it's true

Common inequality mistakes that catch students out

The most frequent mistake is forgetting to flip the inequality sign when multiplying or dividing by a negative—students solve -3x > 12 and incorrectly write x > -4 instead of x < -4. Another widespread error is using the wrong symbol on the number line: writing a closed circle when the inequality is strict (< instead of ≤), or vice versa. When graphing two-variable inequalities, students often shade the wrong region or forget to distinguish between a solid line (≤ or ≥) and a dashed line (< or >). Some also mix up the direction of the inequality when rearranging: rearranging 5 - x > 2 often trips students, especially handling the negative sign on x correctly. Incomplete solutions are common too—writing x < 5 without shading or marking the number line.

• Sign flip reminder: -3x > 12 becomes x < -4, not x > -4—pause and verify this step every time
• Symbol on the number line: ≤ and ≥ get closed circles (filled); < and > get open circles (empty)
• Two-variable inequalities: dashed line for < or >, solid line for ≤ or ≥, then shade the correct region
• Rearranging with negative coefficients: moving -x to the right side and flipping signs is error-prone—work carefully
• Compound inequalities must satisfy all conditions: -2 < x ≤ 5 means x is between -2 and 5, not one or the other
• Forgetting to represent the solution—whether on a number line, as interval notation, or as a shaded region

Frequently asked questions about Inequality Solver