How do you solve $abs(4x - 2) = 10$ ?

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Answer 1 · 2015-08-08T20:44:29

$x = 3$ or $x=-2$ .

You're dealing with an absolute value equation, which means that you need to take into account two possibilities for the modulus

$|4x-2| = 4x-2$

and the equation becomes

$4x-2 = 10$

$4x = 12 implies x = 12/4 = color(green)(3)$

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

and the equation becomes

$-4x+2 = 10$

$-4x = 8 implies x = 8/(-4) = color(green)(-2)$

So, your equation has two possible solutions: $x=3$ or $x=-2$ .

How do you solve abs(4x - 2) = 10 abs(4x - 2) = 10 ?