What to do
A one-step inequality asks you to isolate the variable using a single inverse operation. The answer is usually a range of values, not just one number.
Method
- Identify the operation attached to the variable: addition, subtraction, multiplication, or division.
- Undo it with the opposite operation on both sides of the inequality.
- If a number is added, subtract it.
- If a number is subtracted, add it.
- If the variable is multiplied by a number, divide by that number.
- If the variable is divided by a number, multiply by that number.
- Keep the inequality sign correct.
- If you multiply or divide by a negative number, reverse the inequality sign.
- Simplify the final statement as much as possible.
Check your answer
Test a value from your solution set in the original inequality. It should make the inequality true. Also test a value outside the set to see that it fails.
Example pattern
If the inequality is of the form x + a > b, subtract a from both sides. If it is -3x ≤ 12, divide by -3 and reverse the sign.
Common mistake
Forgetting to flip the inequality sign when dividing or multiplying by a negative number.