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. For example, in the inequality 2x + 3 > 7, you would first subtract 3 from both sides and then divide by 2.

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 solution to the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides to get -4x ≤ 40, then divide by -4 (flipping the sign) to find x ≥ -10.

Front

When do you flip the sign in an inequality?

Back

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

Front

Solve 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 difference between ≤ and < in inequalities?

Back

The symbol ≤ means 'less than or equal to', while < means 'less than' only.

Front

What does the solution x ≥ 3 represent on a number line?

Back

It represents all numbers to the right of 3, including 3 itself.

Front

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

Back

You can check by substituting a number from the solution set back into the original inequality to see if it holds true.