Four times a number, increased by one, is between negative seven and seventeen. Find all the numbers

The numbers are:

{-1, 0, 1, 2, 3}

Step-by-step explanation:

Note: I am assuming "between" does not include the endpoints.

Given the statement

'Four times a number, increased by one, is between negative seven and seventeen'

Let us break down the word statement into small pieces and then combine them to write it into an algebraic expression.

Let x be the number.

4 times a number = 4x

Increase by 1 = 4x+1

between negative seven and seventeen ⇒   -7 < 4x+1  < 17

Thus, the combined statement can be written in an algebraic expression.

-7 < 4x+1  < 17

solving the inequality expression

Add -1 to all parts

Divide all parts by 4

Thus, the numbers are:

{-1, 0, 1, 2, 3}

i.e

The graph is also attached below.

d

step-by-step explanation: