How do you solve #12( - 10x - 14) = 32( x + 4)#?

1 Answer
smendyka
Jan 27, 2017

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis:

#(12 xx -10x) - (12 xx 14) = (32 xx x) + (32 xx 4)#

#-120x - 168 = 32x + 128#

Next, add #color(red)(120x)# and subtract #color(blue)(128)# from each side of the equation to isolate the #x# terms while keeping the equation balanced:

#-120x - 168 + color(red)(120x) - color(blue)(128) = 32x + 128 + color(red)(120x) - color(blue)(128)#

#-120x + color(red)(120x) - 168 - color(blue)(128) = 32x + color(red)(120x) + 128 - color(blue)(128)#

#0 - 168 - 128 = (32 + 120)x + 0#

#-296 = 152x#

Now, divide each side of the equation by #color(red)(160)# to solve for #x# while keeping the equation balanced:

#-296/color(red)(152) = (152x)/color(red)(152)#

#-(8 xx 37)/(8 xx 20) = (color(red)(cancel(color(black)(152)))x)/cancel(color(red)(152))#

#-(cancel(8) xx 37)/(cancel(8) xx 19) = x#

#-37/19 = x#

#x = -37/19#

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