MathematicsChapter 5: Linear Equations and Inequalities
Absolute Value
|ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c.
Learning objectives
- Define and explain absolute value.
- Apply absolute value to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
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.
Formula
b = c or ax+b
Where / symbols
- 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.
Overview
Learn the idea, then use it:
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.
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.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
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.
In simple words
Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
Key points
- split into two
- c < 0 impossible
- isolate then square
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Absolute Value
Sticky Notes · Quick Revision
Core Idea
- |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c.
Key Points
- split into two
- c < 0 impossible
- isolate then square
Simple Check
- Explain absolute value in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge absolute value with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- |ax+b| = c with c>=0 splits into ax+b = c or ax+b = -c.
- split into two
- c < 0 impossible
- isolate then square
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