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: 2x + 3 > 7?

Back

Subtract 3 from both sides: 2x > 4. Then divide by 2: x > 2.

Front

What does it mean when an inequality is written as x < 5?

Back

It means that x can be any number less than 5.

Front

What is the solution to the inequality: -3x ≤ 9?

Back

Divide both sides by -3 (remember to flip the inequality): x ≥ -3.

Front

How do you graph the solution set of an inequality?

Back

Use a number line, draw an open circle for < or >, and a closed circle for ≤ or ≥. Shade the region that represents the solution.

Front

What is the first step in solving the inequality: 5n - 2 > 3?

Back

Add 2 to both sides: 5n > 5.

Front

What does the inequality x + 4 < 10 represent?

Back

It represents that x can be any number less than 6.

Front

How do you isolate the variable in the inequality: 4n + 1 ≥ 13?

Back

Subtract 1 from both sides: 4n ≥ 12, then divide by 4: n ≥ 3.

Front

What is the solution to the inequality: 3(n - 2) < 9?

Back

Divide both sides by 3: n - 2 < 3, then add 2: n < 5.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality, such as x < x.