MathematicsChapter 5: Linear Equations and Inequalities
Variables Both Sides
When x appears on both sides, gather like terms.
Learning objectives
- Define and explain variables both sides.
- Apply variables both sides to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2x-7=5, then add 7 to get 2x=12, so x=6. You can just as well move constants first. The aim is one x term and one number. If the x terms cancel and you are left with 0=8, there is no solution; if you are left with 0=0, every real number works (that case is not a genuine ax+b=0 with a!=0).
Mathematical form
x=6. You can just as well move constants f
b=0 with a
Where / symbols
- Variables Both Sides
- When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2x-7=5, then add 7 to get 2x=12, so x=6. You can just as well move constants first. The aim is one x term and one number. If the x terms cancel and you are left with 0=8, there is no solution; if you are left with 0=0, every real number works (that case is not a genuine ax+b=0 with a!=0).
Relationship
- x=6
Overview
Learn the idea, then use it:
Core Understanding
When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2x-7=5, then add 7 to get 2x=12, so x=6. You can just as well move constants first. The aim is one x term and one number. If the x terms cancel and you are left with 0=8, there is no solution; if you are left with 0=0, every real number works (that case is not a genuine ax+b=0 with a!=0).
Examples both sides · like terms · x=6 · VARIABLES BOTH SIDES: When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2x-7=5, then add 7 to
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 — VARIABLES BOTH SIDES
When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2x-7=5, then add 7 to get 2x=12, so x=6. You can just as well move constants first. The aim is one x term and one number. If the x terms cancel and you are left with 0=8, there is no solution; if you are left with 0=0, every real number works (that case is not a genuine ax+b=0 with a!=0).
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 variables both sides with a neighbouring idea that uses a different definition, rule, or method.
Key points
- both sides
- like terms
- x=6
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Variables Both Sides
Sticky Notes · Quick Revision
Core Idea
- When x appears on both sides, gather like terms.
Key Points
- both sides
- like terms
- x=6
Simple Check
- Explain variables both sides 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 variables both sides 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
- When x appears on both sides, gather like terms.
- both sides
- like terms
- x=6
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