Linear Inequality Solver

Enter a linear inequality of the form ax+b compared with 0 to find the solution range, boundary value, and direction, shown on a number line.

Input

Solve the linear inequality ax+b compared with 0. Enter the coefficients a and b and choose the relation.

Coefficient a

x +

Coefficient b

Relation

Solving: 2 x + -6 > 0

Solution

Solution range for x

x > 3

Boundary value

Direction

Greater than boundary

Boundary included

Subtract b from both sides and divide by a. When a is negative, the inequality direction flips.

For ax+b compared with 0, subtract b from both sides and divide by a to solve for x. The boundary value is x = -b / a.
When the coefficient a is negative, dividing both sides by a negative number flips the inequality direction (greater becomes less, at least becomes at most).
When a is 0, x drops out of the expression and the result depends only on b and the chosen relation. It is either always true or never true.
On the number line the solution region is drawn as a thick segment. A filled dot marks a boundary that is included (at least or at most), and an open dot marks a boundary that is excluded (greater or less).

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