Linear equations in one unknown · Ages 12–13
Equations with brackets
Outside number times every term; a minus flips every sign.
How to do it
Method
Outside number times every term; a minus flips every sign
3(x + 2) = 21, 3x + 6 = 21, x = 5
Another way
Bracket as one thing
3(x + 2) = 21, x + 2 = 7, x = 5
In full
One way: open the brackets first. The number outside multiplies every term inside: 3(x + 2) = 3x + 6; a minus in front changes the sign of every term inside: 10 − 2(x − 1) = 10 − 2x + 2. Another: treat the bracket as one thing. 3(x + 2) = 21; divide both sides by 3, x + 2 = 7, x = 5. That second way is neatest when the other side is a multiple of the outside number; otherwise fractions appear, and opening first is easier. The answers agree.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Which is 18 − 7(x − 5) opened up correctly?
- A. 18 − 7x + 35
- B. 18 + 7x − 35
- C. 18 − 7x + 5
- D. 18 − 7x − 35
Choose the right answer
Show the answer and working
Answer: A. 18 − 7x + 35
−7 times x is −7x, and −7 times −5 is +35.
Example 2
5(x − 16) = 8(x − 4), x =
Show the answer and working
Answer: −16
Open up: 5x − 80 = 8x − 32. Move terms: −80 + 32 = 8x − 5x, so 3x = −48, x = −16.
Example 3
4[3(x − 3) + 1] = −80, x =
Show the answer and working
Answer: −4
Peel from outside in: 3(x − 3) + 1 = −20, 3(x − 3) = −21, x − 3 = −7, x = −4.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.3(x + 8) opens up to 3x + 8.
True or false?
Answer:
2.9(x − 6) = 81, x =
Answer:
3.35 − 5(x − 6) = 20, x =
Answer:
4.2[3(x − 3) + 11] = −38, x =
Answer:
5.3(x − 4) = 6(x − 1), x =
Answer:
All the answers
- 1. False
- 2. 15
- 3. 9
- 4. −7
- 5. −2
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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