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

Front

When solving the inequality 3 ≥ 12 - x, what do you need to do first?

Back

You need to isolate the variable x by first subtracting 12 from both sides.

Front

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

Back

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

Front

How do you represent the solution of an inequality on a number line?

Back

You use a closed circle for 'greater than or equal to' (≥) and 'less than or equal to' (≤), and an open circle for 'greater than' (>) and 'less than' (<).

Front

What is the solution to the inequality 5 + x ≥ 29?

Back

x ≥ 24.

Front

In the inequality -2x + 2 ≥ 12, what is the first step to solve for x?

Back

Subtract 2 from both sides to get -2x ≥ 10.

Front

What does the solution x < 5 look like on a number line?

Back

An open circle at 5 with a line extending to the left.

Front

What is the importance of flipping the inequality sign?

Back

Flipping the inequality sign is crucial when multiplying or dividing by a negative number to maintain the truth of the inequality.

Front

How do you check if your solution to an inequality is correct?

Back

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

Front

What does the inequality z ≥ -4 mean?

Back

It means z can be any number greater than or equal to -4.