Answer :
x - the number
[tex]3 \leq x-9 \leq 8 \\ \\ 3 \leq x-9 \\ 3+9 \leq x \\ 12 \leq x \\ and \\ x-9 \leq 8 \\ x \leq 8+9 \\ x \leq 17 \\ \Downarrow \\ 12 \leq x \leq 17 \\ x \in [12, 17][/tex]
[tex]3 \leq x-9 \leq 8 \\ \\ 3 \leq x-9 \\ 3+9 \leq x \\ 12 \leq x \\ and \\ x-9 \leq 8 \\ x \leq 8+9 \\ x \leq 17 \\ \Downarrow \\ 12 \leq x \leq 17 \\ x \in [12, 17][/tex]
For this case what we must do is find the compound inequality.
To do this, we must first define a variable.
We have then:
x: unknown number.
We write the inequations now:
[tex] x-9 \leq 8 [/tex]
[tex] x-9\geq 3
[/tex]
Therefore, the compound inequation is:
[tex] 3 \leq x-9 \leq 8
[/tex]
The solution of the inequality is:
Inecucción 1:
[tex] x-9 \leq 8
[/tex]
[tex] x \leq 8 + 9 [/tex]
[tex] x \leq 17
[/tex]
Inequality 2:
[tex] x-9\geq 3
[/tex]
[tex] x\geq 3 + 9
[/tex]
[tex] x\geq 12
[/tex]
Then, the solution is:
x ∈ [12, 17]
Answer:
The compound inequation is:
[tex] 3 \leq x-9 \leq 8
[/tex]
The solution is:
x ∈ [12, 17]
