Solve 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 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What does the inequality 11 > -3y + 2 mean?

Back

It means that -3y + 2 is less than 11. To solve, subtract 2 from both sides: 9 > -3y, then divide by -3 (remember to flip the inequality): y < -3.

Front

How do you graph the solution of an inequality?

Back

To graph an inequality, draw a number line, use an open circle for < or > (not including the number) and a closed circle for ≤ or ≥ (including the number). Shade the region that satisfies the inequality.

Front

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

Back

Add 1 to both sides: -9a < 27. Then divide by -9 (flip the inequality): a > -3.

Front

What does the inequality u/7 - 1 ≤ 1 represent?

Back

It represents that u/7 is less than or equal to 2. To solve, add 1 to both sides: u/7 ≤ 2, then multiply by 7: u ≤ 14.

Front

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

Back

Subtract 1 from both sides: -4x > 20. Then divide by -4 (flip the inequality): x < -5.

Front

What is the difference between < and ≤ in inequalities?

Back

< means 'less than' and does not include the number, while ≤ means 'less than or equal to' and includes the number.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by adding or subtracting a constant from both sides.

Front

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

Back

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