How do you solve #|8x + 4| = 52#?

1 Answer
Gazza
Oct 30, 2017

#x=6 or x=-7#

Explanation:

#|8x +4|=52#
Solve for the absolute value
We know either #8x + 4=52 or 8x +4 = -52#
We gonna call the first one possibility ONE and the second one possibility TWO.

Let's start by solving the first possibility
#8x + 4 =52#
Subtract #color(red)(4)# from both sides
#8x cancel(+4) cancelcolor(red)(-4) = 52 - color(red)(4)#
#8x = 48#
Divide both sides #8#
#(cancel8x)/cancel8 = 48/8#
#x= 6#

Then, solve the second possibility
#8x +4=-52#
Let's start by subtracting #color(red)(4)# from both sides
#8x cancel(+4) cancelcolor(red)(-4)= -52 - color(red)(4)#
#8x = -56#
Divide both sides by #8#
#(cancel8x)/cancel8 = (-56)/8#
#x= -7#

Thus,

The answer is #x=6 or x=-7#

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