Question

How do you solve and graph `abs(a-5)<3`?

Answer 1

`2 < a <8`

Explanation:

The standard form for `|x| < a` is.

`-a < x < a`

This is used in the question here.

`rArr-3 < a-5 < 3`

Isolate a in the centre interval by adding 5 to ALL 3 intervals.

`rArr-3+5 < acancel(-5)cancel(+5) < 3+5`

`rArr2 < a < 8larr" is the solution"`

To show the solution on a number line place `color(blue)"open circles"` at 2 and 8 to indicate that 2 and 8 are not values in the solution. If they were we use a solid circle to denote they are part of the solution.

The solution is the values `color(blue)"between"` 2 and 8 which is denoted by a heavy line drawn between the 2 open circles.