Spot the slip
A friend writes 3(x + 5) in a shorter form, 3x + 5. Is that right?
Loading lab…
Step 1 of 5
- The claim: 3(x + 5) = 3x + 5.
- Put in x = 2. Left side: 3 × 7 = 21.
- Right side: 3 × 2 + 5 = 11.
- 21 and 11 differ. It is a mistake.
- The fix, 3x + 15, gives 21.
No. 3(x + 5) is 3x + 15, not 3x + 5.
The rule
A simplified line is a shorter form of an expression. A bracket is the ( ) round some terms.
To test a simplified line, put the same number into both sides. Different answers mean a mistake. One match proves nothing.
Three slips are common. A slip is a small mistake.
| Slip | Example | Right form |
|---|---|---|
| A number outside a bracket multiplies one term only | 3(x + 5) is not 3x + 5 | 3x + 15 |
| A minus before a bracket changes one sign only | 9 − (4 − m) is not 5 − m | 5 + m |
| Terms that are not alike are joined | 4n + 6 is not 10n | 4n + 6 |
3(x + 5) is x + 5 taken three times. That makes 3x + 15. A number outside a bracket multiplies every term inside. A minus before a bracket changes every sign inside.