Compound Inequality Solver

About this calculator

A compound inequality of the form a less than bx + c, and bx + c less than d squeezes the expression bx + c between two bounds at once, and it's solved the same way a single inequality is — by isolating x through valid algebraic operations applied to all three parts simultaneously: first subtract c from every part, then divide every part by b.

The one rule that trips people up is that dividing or multiplying an inequality by a negative number flips its direction — so if b is negative, "a less than (something) less than d" becomes "a greater than (something) greater than d" after dividing, and the bounds swap places accordingly. Getting this sign-flip right is exactly what separates a correctly solved compound inequality from a silently wrong one.