Distributing a negative sign
A minus in front of brackets changes the sign of every term inside.
The common mistake
Changing only the first term: −(x − 4) written as −x − 4 instead of −x + 4.
Instead: Multiply every term inside the brackets by −1 (or by the negative number outside).
Worked example with Guide me
Simplify 10 − 2(x − 3).
- Sugar · What multiplies the brackets, including its sign?Student · −2.
- Sugar · −2 times x, and −2 times −3?Student · −2x and +6.
- Sugar · Now combine with the 10.Student · 10 − 2x + 6 = 16 − 2x.
Answer: 16 − 2x
Try 3 practice questions
1. Simplify −(3x − 5).
Show answer
−3x + 5
2. Simplify 7 − 3(x + 2).
Show answer
1 − 3x
3. Solve 4 − (x − 1) = 2.
Show answer
x = 3
Quick answers
- What is the most common mistake with distributing a negative sign?
- Changing only the first term: −(x − 4) written as −x − 4 instead of −x + 4.
- How do I get distributing a negative sign right?
- Multiply every term inside the brackets by −1 (or by the negative number outside).
- Can you show a worked example?
- Simplify 10 − 2(x − 3). 16 − 2x
Related concepts
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