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 6t + 4 ≤ -2?

Back

Subtract 4 from both sides: 6t ≤ -6. Then divide by 6: t ≤ -1.

Front

What is the solution to the inequality -6 - 3n < -36?

Back

Add 6 to both sides: -3n < -30. Then divide by -3 (remember to flip the inequality): n > 10.

Front

How do you graph the inequality 77 ≤ 5 + 8n?

Back

First, solve for n: 8n ≥ 72, so n ≥ 9. Graph a closed circle at 9 and shade to the right.

Front

What is the solution to the inequality 7 - 3n ≥ -53?

Back

Subtract 7 from both sides: -3n ≥ -60. Then divide by -3: n ≤ 20.

Front

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

Back

Subtract 4 from both sides: 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What does it mean when an inequality is written as n < 10?

Back

It means that n can be any number less than 10.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ means 'less than or equal to', while < means 'less than' only.

Front

How do you check the solution of an inequality?

Back

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

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.