One-Step Linear Inequality - Algebra Step by Step

Solve a linear inequality with a positive coefficient by isolating the variable. The direction of the inequality is preserved at each step because we only add/subtract and divide by a positive number.

solve-linear-inequality To solve ax + b < d with a > 0: subtract b from both sides (direction unchanged), then divide by a (direction unchanged). Express the solution set as an interval.

Example

Solve a linear inequality while preserving the relation symbol.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

2x + 3 < 11

Step 2 — Subtract constant

Subtract 3 from both sides: 11 - 3 = 8.

2x < 11 - 3 = \hl{8}

Step 3 — Divide

Divide by positive 2; keep the sign: 8 / 2 = 4.

x < 8 / 2 = \hl{4}

Step 4 — Interval

Write the interval ending at 4.

x\in(-\infty, \hl{4} )