2 years ago

What is the solution to the inequality below? X^2>=81

Mathematics

1 answer:

kotegsom [21]2 years ago

7 0

Answer:

A. x ≤ - 9 or x ≥ 9

Step-by-step explanation:

x² ≥ 81

| x | ≥ 9

x ≥ 0 => x ≥ 9 => x ∈ [ 9 ; + oo)

x < 0 => x ≤ - 9 => x ∈ ( -oo ; - 9 ]

x ∈ ( -oo ; - 9 ] ∪ [ 9 ; + oo)

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Express f(x) = |x-2| +|x+2| in the non-modulus form. Hence, sketch the graph of f.

alexgriva [62]

Recall that

$|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x$

There are three cases to consider:

(1) When $x+2$ , we have $|x+2|=-(x+2)$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)-(x+2)=-2x-4$

(2) When $x+2\ge0$ and $x-2$ , we get $|x+2|=x+2$ and $|x-2|=-(x-2)$ , so

$|x-2|+|x+2|=-(x-2)+(x+2)=4$

(3) When $x-2\ge0$ , we have $|x+2|=x+2$ and $|x-2|=x-2$ , so

$|x-2|+|x+2|=(x-2)+(x+2)=2x$

So

$|x-2|+|x+2|=\begin{cases}-2x-4&\text{if }x$