Unit 2B Two Step Inequalities/Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality sign): x ≥ -10.

Front

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

Back

You must flip the inequality sign. For example, if you have -2x < 6 and divide by -2, it becomes x > -3.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides: 2k ≤ -10. Then divide by 2: k ≤ -5.

Front

When do you not flip the inequality sign?

Back

You do not flip the inequality sign when you add or subtract a positive or negative number.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

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

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means representing the solution set on a number line, using an open circle for < or > and a closed circle for ≤ or ≥.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ means 'less than or equal to', while < means 'less than'. The former includes the endpoint, while the latter does not.

Front

How do you check if your solution to an inequality is correct?

Back

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

Front

What is the solution set for the inequality x + 5 > 3?

Back

Subtract 5 from both sides: x > -2. The solution set is all numbers greater than -2.