$| x - 3 | \leq 5$
Which of the following inequalities is equivalent to the absolute value inequality above?

- 2 \leq x \leq 8

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- 8 \leq x \leq 8

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x \leq - 2

x \geq 8

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x \leq - 8

x \geq 2

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Solution

The correct option is A $- 2 \leq x \leq 8$
Rule is when $| y | < a$
$\Rightarrow - a < y < a$

Now when $| x - 3 | \leq 5$ , then
$- 7 < 2 x - 3 \leq 5$
Adding 3 and then dividing on both sides, we get
$- 5 + 3 \leq x \leq 5 + 3$
$- 2 < x < 8$

Option $1.$

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