Answer:
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
[tex]-7 < 4x+1 < 17[/tex]
Add -1 to all parts
[tex]-7+-1<4x+1+-1<17+-1[/tex]
[tex]-8<4x<16[/tex]
Divide all parts by 4
[tex]\frac{-8}{4}<\frac{4x}{4}<\frac{16}{4}[/tex]
[tex]-2<x<4[/tex]
Thus, the numbers are:
{-1, 0, 1, 2, 3}
i.e
[tex]-7<4x+1<17\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2<x<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-2,\:4\right)\end{bmatrix}[/tex]
The graph is also attached below.
