Absolute Value Equations
Split into two cases: inside equals ± the value.
Key idea
Split into two cases: inside equals ± the value.
In depth
|x| = a means x is a distance a from zero, so x = a or x = −a. Isolate the absolute value first. If the right side is negative, there is no solution since distance cannot be negative.
Worked example
|2x − 1| = 5: 2x − 1 = 5 → x = 3; 2x − 1 = −5 → x = −2.
Formula
Real-world uses
- Quality control where a part must be within 0.2 mm of a target size
- Tolerance checks
Common mistake
Solving only the positive case.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Absolute Value Equations?
Split into two cases: inside equals ± the value. It is a topic at the intermediate level in Algebra.
What is the formula for Absolute Value Equations?
The key formula is |x| = k ⇒ x = ±k.
Where is Absolute Value Equations used in real life?
Real-world examples: Quality control where a part must be within 0.2 mm of a target size; Tolerance checks.
What should I learn before Absolute Value Equations?
Make sure you are comfortable with Compound Inequalities, the previous topic in Algebra.
What is a common mistake with Absolute Value Equations?
Solving only the positive case.
How can I practise Absolute Value Equations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Absolute Value Equations?
Move on to Absolute Value Inequalities next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.