Question

If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation.

Answer 1

Answer:
`(-9, 16]`

This is the interval from -9 to 16. Exclude -9 but include 16.

=====================================================

Work Shown:

The idea is to multiply all sides by 5, then add 1 to all sides

`-2 < x \le 3`

`5(-2) < 5x \le 5(3)`

`-10 < 5x \le 15`

`-10+1 < 5x+1 \le 15+1`

`-9 < 5x+1 \le 16`

This converts to the interval notation
`(-9, 16]`

note: a curved parenthesis means "do not include this value in the solution set"; while a square bracket has us include the value. So we exclude -9 and include 16.