12-2-24 Two-Step Inequalities (7.13 ARI)

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, to solve 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

What does the inequality symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the inequality symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

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

Back

The inequality sign flips. For example, if you have -2x > 6 and divide by -2, it becomes x < -3.

Front

What does the phrase 'at least' indicate in an inequality?

Back

The phrase 'at least' indicates a minimum value and is represented by the symbol '≥'. For example, 'at least 5' means x ≥ 5.

Front

How do you solve the inequality 3t + 4 < 10?

Back

First, subtract 4 from both sides: 3t < 6. Then, divide by 3: t < 2.

Front

What is the solution to the inequality 5 > 2x - 1?

Back

Add 1 to both sides: 6 > 2x. Then divide by 2: 3 > x or x < 3.

Front

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

Back

Isolating the variable means to get the variable alone on one side of the inequality. This allows you to find the range of values that satisfy the inequality.

Front

What is the first step in solving the inequality 4x - 2 ≤ 10?

Back

The first step is to add 2 to both sides: 4x ≤ 12.

Front

What is the solution to the inequality -3x + 5 > 2?

Back

Subtract 5 from both sides: -3x > -3. Then divide by -3 and flip the sign: x < 1.