# When 4 times a number is subtracted from 5, the

When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.
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Step 1
lets

Cassandra Ramirez
Step 1
Let the number is denoted by x then question says $|5-4x|\le 13$
Thus
$-13\le 5-4x\le 13$
Step 2
Simplify as
$-13-5\le 5-4x-5\le 13-5$
$-18\le -4x\le 8$
$-8\le 4x\le 18$
$-2\le x\le \frac{9}{2}$
$⇒x\in \left[-2,\frac{9}{2}\right]$