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. It often involves addition or subtraction followed by multiplication or division.

Front

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

Back

Add 10 to both sides: 25 + 10 < X, which simplifies to 35 < X or X > 35.

Front

When graphing the inequality b < 6, what type of circle is used?

Back

An open circle is used to indicate that 6 is not included in the solution.

Front

What does the inequality 22 < 6c + 4 represent?

Back

To solve, subtract 4 from both sides: 22 - 4 < 6c, which simplifies to 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

The inequality sign flips. For example, if -3x ≥ 12, dividing by -3 gives x ≤ -4.

Front

How do you represent Samantha's money situation with an inequality?

Back

The inequality is 22.50 + x > 32, where x is the amount of money she received.

Front

What is the solution to the inequality -3x ≥ 12?

Back

x ≤ -4 after dividing both sides by -3 and flipping the sign.

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the number is not included in the solution set.

Front

What is the first step in solving the inequality 5x - 3 < 12?

Back

Add 3 to both sides: 5x < 15.

Front

How do you graph the solution to x > 2?

Back

Draw a number line, place an open circle at 2, and shade to the right.