How do you solve #|8x + 8| + 3 = 35#?

1 Answer
Dec 19, 2016

Answer:

#x = 3# and #x = -5#

Explanation:

First, isolate the absolute value term on one side of the equation by doing the necessary mathematics and keeping the equation balanced:

#abs(8x + 8) + 3 - color(red)(3) = 35 - color(red)(3)#

#abs(8x + 8) + 0 = 32#

#abs(8x + 8) = 32#

Because this problem contains an absolute value term, and the absolute value function transforms a negative or positive number to the positive equivalent we must solve the term in the absolute value for both the positive and negative term the absolute value is equal to:

Solution 1)

#8x + 8 = 32#

#8x + 8 - color(red)(8) = 32 - color(red)(8)#

#8x + 0 = 24#

#8x = 24#

#(8x)/color(red)(8) = 24/color(red)(8)#

#(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = 3#

#x = 3#

Solution 2)

#8x + 8 = color(red)(-)32#

#8x + 8 - color(red)(8) = -32 - color(red)(8)#

#8x + 0 = -40#

#8x = -40#

#(8x)/color(red)(8) = -40/color(red)(8)#

#(color(red)(cancel(color(black)(8)))x)/color(red)(cancel(color(black)(8))) = -5#

#x = -5#