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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).
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Variables Both Sides
What is it?
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).
In simple words
- When x appears on both sides, gather like terms.
- both sides
- like terms
- x=6
Important terms
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).
What you should learn
- 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.
Examples
- both sides
- like terms
- x=6
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).
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
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).
Learn the idea, then use it:
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.
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).
Remember
- both sides
- like terms
- x=6
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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- both sides
- like terms
- x=6
- keep the ideas separate
- both sides
- like terms
- x=6
- correct term
Deeper understanding
Go beyond memorising Variables Both Sides. 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
- both sides
- like terms
- x=6
- keep the ideas separate
- Variables Both Sides: When x appears on both sides, gather like terms. From 4x-7=2x+5 subtract 2x from both sides to get 2
- 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 2
Do not merge variables both sides with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Variables Both Sides: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- both sides
- like terms
- x=6
- keep the ideas separate
Important formulas
- both sides
- like terms
- x=6
Common exam traps
- Do not merge variables both sides 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 variables both sides 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 variables both sides 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.
both sides
like terms
x=6
keep the ideas separate
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
x=6
- 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
- Formula
- x=6
- Example
- both sides
- Critical warning
- Do not merge variables both sides with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Variables Both Sides.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Variables Both Sides and say why it fits.
Mistake
Q4. State one common mistake students make about Variables Both Sides.
Exam note
Q5. Write a short exam note on Variables Both Sides: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.