Question

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

Answer 1

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]`

Answer 2

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`

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Therefore, the compound inequation is:

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The solution of the inequality is:

Inecucción 1:

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`x \leq 8 + 9`

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Inequality 2:

`image`

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Then, the solution is:

x ∈ [12, 17]

Answer:

The compound inequation is:

`image`

The solution is:

x ∈ [12, 17]