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 often involves addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

Front

What does the inequality 2x + 6 ≥ -8 represent?

Back

To solve, subtract 6 from both sides: 2x ≥ -14. Then divide by 2: x ≥ -7.

Front

How do you solve the inequality 2 + 3x ≤ 20?

Back

Subtract 2 from both sides: 3x ≤ 18. Then divide by 3: x ≤ 6.

Front

What is the rule for flipping the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution to the inequality \( \frac{u}{7} - 1 \le 1 \)?

Back

Add 1 to both sides: \( \frac{u}{7} \le 2 \). Then multiply by 7: u ≤ 14.

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

How do you graph the inequality x > -3?

Back

Draw a number line, place an open circle at -3, and shade to the right to indicate all numbers greater than -3.

Front

What is the first step in solving the inequality 2x - 5 < 9?

Back

Add 5 to both sides: 2x < 14.