Practice question · Numerical answer
How many integers x satisfy |x - 4| < 3?
Hints
- Read the inequality as 'the distance from x to 4 is less than 3'.
- That places x strictly between 1 and 7.
Show the answer
5
Why
| x - 4 | < 3 means 1 < x < 7, so the integers are 2, 3, 4, 5, 6, five of them. The endpoints 1 and 7 are excluded because the inequality is strict; including them would give 7, which is the standard off-by-two error. |
Practise Real Numbers and the Number Line
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