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. 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 22 < 6c + 4?

Back

Subtract 4 from both sides to get 18 < 6c, then divide by 6 to find c > 3.

Front

What does the solution k ≤ -5 represent in a two-step inequality?

Back

It means that k can be any number less than or equal to -5.

Front

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

Back

Add 10 to both sides to get 35 < X, which means X > 35.

Front

What is the first step in solving the inequality 2 - 3x ≤ 20?

Back

Subtract 2 from both sides to get -3x ≤ 18.

Front

What is the solution to the inequality -4x + 1 > 21?

Back

Subtract 1 from both sides to get -4x > 20, then divide by -4 (remember to flip the inequality) to find x < -5.

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

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides to get 2k ≤ -10, then divide by 2 to find k ≤ -5.

Front

How do you check the solution of an inequality?

Back

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

Front

What is the graphical representation of an inequality?

Back

An inequality can be represented on a number line with an open or closed circle indicating whether the endpoint is included.