3.3 Solving Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable.

Front

How do you solve the inequality 4x - 2 < 0?

Back

Add 2 to both sides: 4x < 2, then divide by 4: x < 1/2.

Front

What is the solution to the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9, then divide by -3 (flip the sign): x > -3.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

Solve for k: 2k - 9 ≤ -19.

Back

Add 9 to both sides: 2k ≤ -10, then divide by 2: k ≤ -5.

Front

What is the solution to the inequality -24 + k ≤ 10?

Back

Add 24 to both sides: k ≤ 34.

Front

What is the first step in solving the inequality -3x ≥ 12?

Back

Divide both sides by -3 (flip the sign): x ≤ -4.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you check the solution of an inequality?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the difference between < and ≤?

Back

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