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 graph the solution set of an inequality?

Back

To graph the solution set of an inequality, first solve the inequality for the variable, then plot the solution on a number line, using an open circle for < or > and a closed circle for ≤ or ≥.

Front

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

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Front

Solve the inequality: -4a ≤ -28. What is the solution?

Back

a ≥ 7.

Front

Solve the inequality: -4x + 14 ≤ 54. What is the solution?

Back

x ≥ -10.

Front

What is the solution to the inequality: 4(2a + 3) < 3(a - 1)?

Back

a < -3.

Front

Solve the inequality: 14 < -2a + 6 - 2a. What is the solution?

Back

a < -2.

Front

What does it mean to isolate the variable in an inequality?

Back

Isolating the variable means to manipulate the inequality so that the variable is on one side and all other terms are on the opposite side.

Front

What is the first step in solving the inequality: 3x - 5 < 10?

Back

Add 5 to both sides to get 3x < 15.

Front

How do you check your solution for an inequality?

Back

To check your solution, substitute the solution back into the original inequality to see if it makes the inequality true.