Math Solver

Verified real solution sets

Linear Inequality Calculator

Solve a one-variable linear inequality with exact rational arithmetic and verify every displayed transformation against the original real solution set.

Solve an inequalitySee the boundary
Status
Verified
Maximum degree
1
Domain
Real numbers
Independent check
Solution-set equality

The sign change is part of the proof

When the variable coefficient is negative, dividing both sides reverses the comparison. The final half-line is accepted only when it has the same real solution set as the original inequality.

Positive coefficient

2x+3<72x+3<7x<2x<2

Negative coefficient

−2x+3≤7-2x+3\le7x≥−2x\ge-2

Current limitations

  • One variable and one comparison only.
  • Linear expressions with exact rational coefficients.
  • No compound, absolute-value, rational, or quadratic inequalities.
  • All-real and no-solution outcomes are supported when variable terms cancel.

Questions

Linear inequality calculator FAQ

When does the inequality sign reverse?

It reverses when both sides are multiplied or divided by a negative number. Math Solver verifies the resulting real solution set independently.

Which inequality symbols are supported?

The current calculator supports <, <=, >, and >=, including the Unicode symbols ≤ and ≥.

Does it solve compound inequalities?

Not yet. The current verified boundary is one comparison with one variable and linear expressions on each side.