2.4 - Solving Multi-Step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality 9 + 4x > 21?

Back

Subtract 9 from both sides: 4x > 12. Then divide by 4: x > 3.

Front

What does the solution x > 3 represent on a number line?

Back

It represents all numbers greater than 3, which is shown as an open circle at 3 and a line extending to the right.

Front

What is the first step to solve -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40.

Front

What happens when you multiply or divide both sides of an inequality by a negative number?

Back

You must flip the inequality symbol.

Front

Solve the inequality -4a ≤ -28.

Back

Divide both sides by -4 (remember to flip the inequality): a ≥ 7.

Front

What is the solution to the inequality 17 ≤ -2m - 3?

Back

Add 3 to both sides: 20 ≤ -2m. Then divide by -2 (flip the inequality): -10 ≥ m or m ≤ -10.

Front

What does the symbol '≤' mean in an inequality?

Back

It means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

What is the solution set of the inequality x ≥ -10?

Back

The solution set includes all numbers greater than or equal to -10, represented on a number line with a closed circle at -10 and a line extending to the right.

Front

How do you graph the solution set of an inequality?

Back

Identify the boundary point, use an open circle for '>' or '<' and a closed circle for '≥' or '≤', then shade the appropriate side of the number line.