Two Step Inequalities

Front

What is a two-step inequality?

Back

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 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8. Then divide by 2: x < 4.

Front

What is the first step in solving the inequality 5x - 2 > 8?

Back

Add 2 to both sides: 5x > 10.

Front

How do you graph the solution x > 3?

Back

Draw a number line, place an open circle on 3, and shade to the right.

Front

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

Back

The inequality sign flips direction.

Front

Solve and graph the inequality -3x + 4 ≤ 10.

Back

Subtract 4: -3x ≤ 6. Divide by -3 (flip the sign): x ≥ -2. Graph with a closed circle at -2 and shade to the right.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that satisfy the inequality, often resulting in a contradiction.

Front

How do you check your solution for the inequality 4x - 1 < 11?

Back

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

Front

What is the solution to the inequality 2(x - 1) > 6?

Back

Distribute: 2x - 2 > 6. Add 2: 2x > 8. Divide by 2: x > 4.

Front

What does the term 'solution set' refer to in inequalities?

Back

The set of all values that satisfy the inequality.