How do you solve $abs(x+10)=4x-8$ ?

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Answer 1 · 2015-08-02T19:10:29

$x = 6$

$|x+10| = 4x-8$

Right from the start, you know that the solutions to this equation must satisfy the condition

$4x-8>0 <=> x>2$

That happens because the absolute value of a number, regardlesss if that number is positive or negative, is always positive.

$color(blue)( |a| = {(a",", "if " a>=0), (-a",", "if "a<0):})$

So, with this in mind, determine the equation's two possible solutions

$|x+10| = x+10$

and the equation becomes

$x+10 = 4x - 8 => x = 18/3 = color(green)(6)$

$|x+10| = -(x+10) = -x-10$

This will get you

$-x-10 = 4x+8 => x = color(red)(-18/5)$

This solution, $x=-18/5$ , will be an extraneous solution because it does not satisfy the contion $x>2$ .

Therefore, $x=6$ is the only solution to this equation.

How do you solve abs(x+10)=4x-8abs(x+10)=4x-8?