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: 2 - 3x ≤ 20?

Back

First, subtract 2 from both sides: -3x ≤ 18. Then, divide by -3 (remember to flip the inequality): x ≥ -6.

Front

What does it mean when an inequality has a 'greater than' symbol?

Back

It means that the value on the left side is larger than the value on the right side.

Front

Solve the inequality: -6 - 3n < -36.

Back

Add 6 to both sides: -3n < -30. Then divide by -3: n > 10.

Front

What is the solution to the inequality: 6t + 4 ≤ -2?

Back

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

Front

How do you graph the inequality: k ≤ -5?

Back

Draw a number line, place a closed circle on -5, and shade to the left to indicate all numbers less than or equal to -5.

Front

What is the first step in solving the inequality: 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10.

Front

What does the solution n < 10 represent?

Back

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

Front

Solve and graph the inequality: 7n - 1 > 76.

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11. Graph with an open circle at 11 and shade to the right.

Front

What is the difference between '≤' and '<'?

Back

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