How do you solve the absolute value inequality and express the solution set in interval notation for $- 2 | s - 3 | < - 4$ $-2abs(s-3)<-4$ ?

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How do you solve the absolute value inequality and express the solution set in interval notation for $- 2 | s - 3 | < - 4$ $-2abs(s-3)<-4$ ?

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Answer 1 · 2015-04-10T15:38:31

Multiplying both sides of an inequality by a negative value reverses the inequality
So
$- 2 | s - 3 | < - 4$ $-2abs(s-3) < -4$
is equivalent to
$| s - 3 | > 2$ $abs(s-3) > 2$

If $(s - 3)$ $(s-3)$ is negative (i.e. $s < 3$ $s<3$ )
then this becomes
$3 - s > 2$ $3-s > 2$
$- s ≻ 1$ $-s>-1$
$s < 1$ $s<1$

If $(s - 3)$ $(s-3)$ is positive or zero (i.e. $s \geq 3$ $s>=3$ )
then
$(s - 3) > 2$ $(s-3)>2$
$s > 5$ $s>5$

So
$s ε (- \infty, 1) ⋃ (5, + \infty)$ $s epsilon (-oo,1)uuu(5,+oo)$

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How do you solve the absolute value inequality and express the solution set in interval notation for $- 2 | s - 3 | < - 4$ $-2abs(s-3)<-4$ ?

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How do you solve the absolute value inequality and express the solution set in interval notation for −2|s−3|<−4-2abs(s-3)<-4?

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How do you solve the absolute value inequality and express the solution set in interval notation for $- 2 | s - 3 | < - 4$ $-2abs(s-3)<-4$ ?