Multi Step Inequalities

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

First, distribute: $$3k - 15 + 9k ≥ -3$$ . Combine like terms: $$12k - 15 ≥ -3$$ . Add 15 to both sides: $$12k ≥ 12$$ . Finally, divide by 12: $$k ≥ 1$$ .

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Combine like terms: $$-5p > -10$$ . Divide by -5 (flip the sign): $$p < 2$$ .

Distribute: $$4y - 16 + 8 ≤ 20$$ . Combine like terms: $$4y - 8 ≤ 20$$ . Add 8 to both sides: $$4y ≤ 28$$ . Divide by 4: $$y ≤ 7$$ .

Distribute: $$-3x - 12 + 3 ≥ 9$$ . Combine like terms: $$-3x - 9 ≥ 9$$ . Add 9 to both sides: $$-3x ≥ 18$$ . Divide by -3 (flip the sign): $$x ≤ -6$$ .

The first step is to simplify both sides of the inequality, which may include distributing, combining like terms, or moving terms to one side.

The inequality sign flips direction when you multiply or divide both sides by a negative number.

Yes, divide by -3 (flip the sign): $$x ≤ -4$$ .

Subtract 3 from both sides: $$2x < 8$$ . Divide by 2: $$x < 4$$ .