How do you solve $| 5 k + 4 | \geq 36$ $abs(5k+4)>=36$ ?

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How do you solve $| 5 k + 4 | \geq 36$ $abs(5k+4)>=36$ ?

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Answer 1 · 2017-11-24T13:50:58

$(- \infty, - 8] \cup [\frac{32}{5}, + \infty)$ $(-oo,-8]uu[32/5,+oo)$

Explanation:

$inequalities of the type | x | \geq a$ $"inequalities of the type "|x|>=a$
$have solutions of the form$ $"have solutions of the form "$

$x \leq - a OR x \geq a$ $x<=-a" OR "x>=a$

$\Rightarrow 5 k + 4 \leq - 36 or 5 k + 4 \geq 36$ $rArr5k+4<=-36" or "5k+4>=36$

$(1) x 5 k + 4 \leq - 36$ $(1)color(white)(x)5k+4<=-36$

$\Rightarrow 5 k \leq - 40 \Rightarrow k \leq - 8$ $rArr5k<=-40rArrk<=-8$

$(2) x 5 k + 4 \geq 36$ $(2)color(white)(x)5k+4>=36$

$\Rightarrow 5 k \geq 32 \Rightarrow k \geq \frac{32}{5}$ $rArr5k>=32rArrk>=32/5$

$the solution can be expressed in interval notation as$ $"the solution can be expressed in interval notation as"$

$(- \infty, - 8] \cup [\frac{32}{5}, + \infty)$ $(-oo,-8]uu[32/5,+oo)$

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How do you solve $| 5 k + 4 | \geq 36$ $abs(5k+4)>=36$ ?

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How do you solve $| 5 k + 4 | \geq 36$ $abs(5k+4)>=36$ ?