Verified Answer :

naǫ

x - the number

\(3 \leq x-9 \leq 8 \\ \\ 3 \leq x-9 \\ 3+9 \leq x \\ 12 \leq x \\ and \\ x-9 \leq 8 \\ x \leq 8+9 \\ x \leq 17 \\ \Downarrow \\ 12 \leq x \leq 17 \\ x \in [12, 17]\)

carlosego

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:


\(x-9 \leq 8\)


\(x-9\geq 3
\)

Therefore, the compound inequation is:


\(3 \leq x-9 \leq 8
\)

The solution of the inequality is:

Inecucción 1:

\(x-9 \leq 8
\)

\(x \leq 8 + 9\)


\(x \leq 17
\)

Inequality 2:


\(x-9\geq 3
\)

\(x\geq 3 + 9
\)

\(x\geq 12
\)

Then, the solution is:

x ∈ [12, 17]

Answer:

The compound inequation is:

\(3 \leq x-9 \leq 8
\)

The solution is:

x ∈ [12, 17]

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