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Nine less than a number is no more than 8 and is no less than 3.
Compound inequalities

Sagot :

naǫ
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]
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:

[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]

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