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 like addition, subtraction, multiplication, or division.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, just like in equations, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

Solve the inequality: 9 + 4x > 21

Back

x > 3

Front

Solve the inequality: 5x - 6 > 14

Back

x > 4

Front

Solve the inequality: 15 - 10x < 24

Back

x > -0.9

Front

Solve the inequality: 1.8x - 3.4 > 5.6

Back

x > 5

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign reverses when you multiply or divide both sides of the inequality by a negative number.

Front

Solve the inequality: 4(x + 3) = -32

Back

x ≤ -11

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How do you graph a solution to an inequality on a number line?

Back

To graph a solution to an inequality, use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint), then shade the appropriate direction.