How do you graph and solve $4 |4-3x |= 4x + 6$ ?

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Answer 1 · 2016-02-14T00:46:43

Consider that the absolute value can either be positive or negative. As a result, there will be two solutions.

Let's start with the scenario that the absolute value is positive:

$4(4 - 3x) = 4x + 6$

$16 - 12x = 4x + 6$

$10 = 16x$

$5/8 = x$

Negative scenario:

$4(-(4 - 3x)) = 4x + 6$

$4(-4 + 3x) = 4x + 6$

$-16 + 12x = 4x + 6$

$-22 = -8x$

$11/4 = x$

The solution set is $x = 5/8 and 11/4$ .

Practice exercises:

Solve $2 - |2x + 5| - 4x = 3x - 8$

How do you graph and solve 4 |4-3x |= 4x + 64 |4-3x |= 4x + 6?