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: -3 − 6(4x + 6) > -111. What is the solution?

Back

x < 3.

Front

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

Back

x < 1.

Front

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

Back

x ≥ -10.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify both sides of the inequality if necessary, which may involve distributing or combining like terms.

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 difference between < and ≤ in inequalities?

Back

< means 'less than' and does not include the endpoint, while ≤ means 'less than or equal to' and includes the endpoint.