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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 5x - 7 ≥ 8?

Back

Add 7 to both sides to get 5x ≥ 15, then divide by 5 to find 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 the inequality 9x - 3 > 6.

Back

Add 3 to both sides to get 9x > 9, then divide by 9 to find x > 1.

Front

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

Back

The first step is to divide both sides by -3, which requires flipping the inequality sign, resulting in x ≤ -4.

Front

How do you graph the solution to the inequality x > 3?

Back

Draw a number line, place an open circle on 3, and shade to the right to indicate all numbers greater than 3.

Front

What is the solution to the inequality 4x - 4 > 8?

Back

Add 4 to both sides to get 4x > 12, then divide by 4 to find x > 3.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

Add 1 to both sides to get 7n > 77, then divide by 7 to find n > 11.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values satisfy the original inequality and helps confirm that the solution is correct.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that can satisfy the inequality, often resulting in a contradiction.