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

Front

How do you solve the inequality 2 - 3x ≤ 20?

Back

To solve 2 - 3x ≤ 20, first subtract 2 from both sides to get -3x ≤ 18, then divide by -3 (remember to flip the inequality sign) to find x ≥ -6.

Front

What does it mean to flip the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign means that if you divide or multiply both sides of an inequality by a negative number, the direction of the inequality changes.

Front

How do you interpret the solution x ≥ 3?

Back

The solution x ≥ 3 means that x can be any number greater than or equal to 3.

Front

What is the solution to the inequality 11 > -3y + 2?

Back

To solve 11 > -3y + 2, subtract 2 from both sides to get 9 > -3y, then divide by -3 (flipping the sign) to find y > -3.

Front

What does the inequality x < -20 represent on a number line?

Back

The inequality x < -20 represents all numbers to the left of -20 on a number line, not including -20 itself.

Front

How do you solve the inequality 25 < x - 10?

Back

To solve 25 < x - 10, add 10 to both sides to get 35 < x, or x > 35.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What are the steps to graph a solution to a two-step inequality?

Back

1. Solve the inequality for the variable. 2. Determine the type of circle (open or closed) based on the inequality sign. 3. Shade the appropriate region on the number line.

Front

What does the term 'solution set' refer to in the context of inequalities?

Back

The solution set is the set of all values that satisfy the inequality.