Linear equations in one unknown · Ages 12–13
Unknowns on both sides
Cross the equals sign, change the sign.
How to do it
Method
Cross the equals sign, change the sign
5x + 3 = 2x + 15, 5x − 2x = 15 − 3, x = 4
Another way
Take from both sides
Take 2x from both: 3x + 3 = 15
In full
When x is on both sides, gather the x terms on one side and the numbers on the other. By the balance: 5x + 3 = 2x + 15; take 2x from both sides, 3x + 3 = 15; take 3 from both, 3x = 12, x = 4. Moving terms is its shorthand: a term that crosses the equals sign changes its sign, 5x − 2x = 15 − 3, 3x = 12, x = 4. The two match step for step. Move the smaller x term and x's coefficient stays positive, which leaves less room for slips.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
−31 − 5x = 9x − 17, x =
Show the answer and working
Answer: −1
Move the x terms right and the numbers left: −31 + 17 = 9x + 5x, so 14x = −31 + 17, x = −1.
Example 2
Moving terms in 13x − 5 = 7x + 20, which line is right?
- A. 13x − 7x = 20 − 5
- B. 13x + 7x = 20 − 5
- C. 13x + 7x = 20 + 5
- D. 13x − 7x = 20 + 5
Choose the right answer
Show the answer and working
Answer: D. 13x − 7x = 20 + 5
Each term changes sign as it crosses: 7x to −7x and −5 to +5.
Example 3
9x − 4 = 7x + 14, x =
Show the answer and working
Answer: 9
7x crosses to the left and −4 to the right, each changing sign: 9x − 7x = 14 + 4, 2x = 18, x = 9.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.12x + 12 = 6x + 48: moving terms, x = , so x = .
Fill in each blank
Answer:
2.Moving terms in 13x − 7 = 7x + 11, which line is right?
- A. 13x + 7x = 11 + 7
- B. 13x − 7x = 11 + 7
- C. 13x + 7x = 11 − 7
- D. 13x − 7x = 11 − 7
Choose the right answer
Answer:
3.−74 − 6x = 3x − 20, x =
Answer:
4.12x + 9 = 4x + 5, x =
Answer in simplest form
Answer:
5.7x − 31 = 3x + 5, x =
Answer:
All the answers
- 1. 6, 36, 6
- 2. B. 13x − 7x = 11 + 7
- 3. −6
- 4. −12
- 5. 9
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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