Solving & Graphing 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 combining like terms, distributing, and isolating the variable.

Front

What does the inequality sign '≤' mean?

Back

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

Front

What does the inequality sign '≥' mean?

Back

The '≥' sign means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

How do you graph the inequality x < 4 on a number line?

Back

Draw a number line, place an open circle at 4 (indicating 4 is not included), and shade to the left to show all numbers less than 4.

Front

How do you graph the inequality x ≥ -4 on a number line?

Back

Draw a number line, place a closed circle at -4 (indicating -4 is included), and shade to the right to show all numbers greater than or equal to -4.

Front

What is the first step to solve the inequality -2n - 3 < 2n + 9?

Back

The first step is to add 2n to both sides to combine like terms.

Front

What is the solution to the inequality -3x + 2 ≤ 20?

Back

The solution is x ≥ -6.

Front

When solving inequalities, when do you flip the inequality sign?

Back

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

Front

What is the solution to the inequality 3x ≥ -12?

Back

The solution is x ≥ -4.

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 other side.