Linear Inequality Solver
Enter the coefficients and choose an inequality symbol to solve ax + b [symbol] c for x.
Last updated: September 5, 2026
Frequently asked questions
How do I solve a linear inequality like 2x + 3 > 7?
Isolate x the same way as an equation: subtract 3 from both sides to get 2x > 4, then divide by 2 to get x > 2. The only special rule is that dividing or multiplying by a negative number flips the inequality's direction.
Why does the inequality sign flip when dividing by a negative number?
Because multiplying or dividing by a negative reverses the order of numbers on the number line - if 2 < 3, multiplying both sides by −1 gives −2 and −3, and −2 is actually greater than −3, so the inequality must flip to stay true (−2 > −3).
What does 'no solution' or 'all real numbers' mean for an inequality?
This happens when the x term cancels out (a = 0), leaving just a comparison of two numbers - if that comparison is always true (like 5 > 3), every x satisfies it; if it's never true (like 3 > 5), no x does, since x never had any influence on the outcome.
How is solving an inequality different from solving an equation?
The steps are almost identical (isolate x by adding, subtracting, multiplying, or dividing on both sides), with one key exception: multiplying or dividing both sides by a negative number flips the inequality symbol's direction.
What's the solution to −2x + 3 ≤ 7?
x ≥ −2 - subtract 3 from both sides to get −2x ≤ 4, then divide by −2 and flip the symbol (since you divided by a negative): x ≥ −2.
How do I graph the solution to an inequality on a number line?
Use an open circle for < or > (the boundary value itself isn't included) and a filled circle for ≤ or ≥ (the boundary is included), then shade the number line in the direction the inequality points from that circle.