6 min read
Absolute Value
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
Choose Your Level
Absolute Value
What is it?
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
In simple words
- |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c.
- split into two
- c < 0 impossible
- isolate then square
Important terms
Absolute Value: |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
What you should learn
- Define and explain absolute value.
- Apply absolute value to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Examples
- split into two
- c < 0 impossible
- isolate then square
CORE UNDERSTANDING
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 9
Full school-level explanation
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
Learn the idea, then use it:
WHAT — ABSOLUTE VALUE
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
CORE UNDERSTANDING
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
Remember
- split into two
- c < 0 impossible
- isolate then square
Examples
- split into two
- c < 0 impossible
- isolate then square
- ABSOLUTE VALUE: |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| >
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- split into two
- c < 0 impossible
- isolate then square
- keep the ideas separate
- split into two
- c < 0 impossible
- isolate then square
- correct term
Deeper understanding
Go beyond memorising Absolute Value. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- split into two
- c < 0 impossible
- isolate then square
- keep the ideas separate
- Absolute Value: |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 i
- WHAT — ABSOLUTE VALUE: |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 i
Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Absolute Value: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- split into two
- c < 0 impossible
- isolate then square
- keep the ideas separate
Important formulas
- split into two
- c < 0 impossible
- isolate then square
Common exam traps
- Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
split into two
c < 0 impossible
isolate then square
keep the ideas separate
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
- Definition
- |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c. If c<0, no solution. Inequalities: |x| < 2 is -2 < x < 2. |x| > 2 is x<-2 or x>2. Draw a number line.
- Example
- split into two
- Critical warning
- Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Absolute Value.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Absolute Value and say why it fits.
Mistake
Q4. State one common mistake students make about Absolute Value.
Exam note
Q5. Write a short exam note on Absolute Value: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.