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 typically 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 to get 35 < X, which simplifies to X > 35.

Front

What does the inequality -9a - 1 < 26 represent?

Back

To solve, add 1 to both sides to get -9a < 27, then divide by -9 (remember to flip the inequality) to find a > -3.

Front

What is the solution to the inequality 5x < 5?

Back

Divide both sides by 5 to get x < 1.

Front

How do you isolate the variable k in the equation 16 = k/11?

Back

Multiply both sides by 11 to isolate k, resulting in k = 176.

Front

What does the graph of a ≥ 11 look like?

Back

It includes all values of a that are greater than or equal to 11, represented by a solid dot at 11 and a line extending to the right.

Front

What is the first step in solving the inequality 3x + 4 < 10?

Back

Subtract 4 from both sides to get 3x < 6.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips. For example, if -2x < 4, dividing by -2 gives x > -2.

Front

What is the solution set for the inequality x - 5 > 2?

Back

Add 5 to both sides to get x > 7.

Front

How do you represent the solution to the inequality 2x + 3 ≤ 11 on a number line?

Back

The solution x ≤ 4 is represented by a solid dot at 4 and a line extending to the left.