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#