2-step Inequalities

Front

What is a 2-step inequality?

Back

A 2-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 3x + 4 > 13?

Back

Subtract 4 from both sides to get 3x > 9, then divide by 3 to find x > 3.

Front

What is the first step in solving the inequality -9a - 1 < 26?

Back

Add 1 to both sides to get -9a < 27.

Front

What is the solution to the inequality 7b - 3 < 11?

Back

Add 3 to both sides to get 7b < 14, then divide by 7 to find b < 2.

Front

How do you isolate x in the inequality x/-4 + 2 > 7?

Back

Subtract 2 from both sides to get x/-4 > 5, then multiply by -4 (remember to flip the inequality) to find x < -20.

Front

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

Back

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

Front

What is the solution to the inequality -9a - 1 < 26?

Back

The solution is a > -3.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values satisfy the original inequality, confirming that the solution is correct.

Front

What is the general form of a 2-step inequality?

Back

A 2-step inequality generally takes the form of ax + b < c or ax + b > c, where a, b, and c are constants.

Front

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

Back

You can represent the solution by shading the region of the number line that satisfies the inequality and using open or closed circles to indicate whether endpoints are included.