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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -9a - 1 < 26?

Back

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

Front

What is the solution to the inequality -3x - 4 < 5?

Back

Add 4 to both sides to get -3x < 9, then divide by -3 (flip the inequality sign) to find x > -3.

Front

How do you solve the inequality -4x + 1 > 21?

Back

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

Front

What does the inequality -4x + 14 ≤ 54 represent?

Back

It represents that the expression on the left is less than or equal to 54, and solving it gives x ≥ -10.

Front

How do you interpret the inequality 22 < 6c + 4?

Back

This means that 6c + 4 must be greater than 22, and solving it gives c > 3.

Front

What is the importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary to maintain the truth of the inequality when multiplying or dividing by a negative number.

Front

What are the steps to graph a solution to a two-step inequality?

Back

1. Solve the inequality for the variable. 2. Identify the boundary point. 3. Use an open or closed circle based on the inequality sign. 4. Shade the appropriate side of the number line.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality, often resulting from contradictory statements.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.