How do you solve $|-4x + -1| = 33$ ?

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Answer 1 · 2016-06-27T18:11:51

$x = - 17/2$ and $x = 8$

$|-4x -1| = 33$

let's assume that $-4x-1 >0$ so #|-4x - 1| = -4x -1

so we look at
$-4x -1 = 33 \implies 4x = -34 \implies x = - 17/2$

then let's assume that in fact $-4x-1 <0$ so $|-4x - 1| = 4x+ 1$

so here instead we look at
$4x +1 = 33 \implies 4x = 32 \implies x = 8$

How do you solve |-4x + -1| = 33|-4x + -1| = 33?