You can add and subtract values from both sides of an inequality in the same way as an equation.

Solve x + 12 > 15.

Step 1: Decide what needs to be removed to get the variable x by itself. You need to remove the “+ 12.”

x + 12 > 15

Step 2: Remove the “1 12” by doing the opposite, or inverse, operation. Subtract 12 from each side of the inequality.

x + 12 – 12 > 15 – 12
x > 3

Step 3: Test your answer. Check any number from the solution set. Let’s check the number 5.

5 + 12 > 15
17 > 15 True

Check a number that is not part of the solution set. Let’s check 0.

0 + 12 > 15
12 > 15 Not True

Know your calculator. If you’re using someone else’s calculator, make sure you understand how to use it before you begin a test.

Solve and graph the inequality x – 2 < 1.

Step 1: Decide what needs to be removed to get the variable x by itself. You need to remove the “– 2.” Add 2 to each side of the inequality.

x – 2 < 1
x – 2 + 2 < 1 + 2
x < 3

Step 2: Graph the inequality x < 3 on a number line.

Step 3: Test your answer. Check any number from the solution set. Let’s check the number 0.

0 – 2 < 1
^–2 < 1 True

Check a number that is not part of the solution set. Let’s check 3.

3 – 2 < 1
1 < 1 Not True

Check your solutions whenever you can. In word problems, try putting the answer into the problem.

For the problem above, the solution is more than $34. Test $50. If Casey had $50, and gave $20 away, would he still have more than $14? YES!

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Addition and Subtraction Inequalities