Intro to Expressions and Equations

One-Step Inequalities

Solve an inequality with one inverse operation: x + 3 < 7 → subtract 3 → x < 4.

Example

Solve inequalities with inverse operations while preserving the relation.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x+3<7x+ 3 < 7
Start with x + 3 < 7.x + 37<The variable side has an extra amount added.

Step 2 — Subtract from both sides

Subtract 3 from both sides.

x+3−3<7−3x+ 3 - \hl{3} < 7 - \hl{3}
Subtract 3 from both sides; the sign stays <.x + 3 - 37 - 3<subtract 3subtract 3Same subtraction on both sides preserves the inequality direction.

Step 3 — Simplify

Simplify both sides: 7 - 3 = 4; the sign stays <.

x<7−3=4x < 7 - 3 = \hl{4}
7 - 3 = 4, so x < 4.x4<The relation is still <: x < 4.

Step 4 — Result

Read the final result.

x<4x < 4
Graph x < 4.012345678open endpoint at 4Because the symbol is <, shade left from 4.
one-step-inequality To solve a one-step inequality: - Apply the same inverse as for equations. - Keep the inequality sign direction. - (Flip direction only when multiplying or dividing by a negative number.)