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 on one side of the inequality sign.

Front

How do you solve the inequality 3x + 2 > 14?

Back

Subtract 2 from both sides to get 3x > 12, then divide by 3 to find x > 4.

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

How do you solve the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -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 (remember to flip the inequality) to find x ≥ -10.

Front

How do you solve the inequality -2x + 7 < 19?

Back

Subtract 7 from both sides to get -2x < 12, then divide by -2 (remember to flip the inequality) to find x > -6.

Front

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

Back

When you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality sign.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by performing the inverse operation (addition or subtraction) on both sides.

Front

Can two-step inequalities have no solution?

Back

Yes, some two-step inequalities can have no solution, such as when the variable cancels out and results in a false statement.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality shows a number line with an open or closed circle at the boundary point and shading to indicate the solution set.