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.

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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.