How do you solve #-3( 2t - 4) + 2t = 4t - 3#?

1 Answer
smendyka
Feb 27, 2017

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term in the parenthesis by #color(red)(-3)#. Be careful to handle the signs of the individual terms correctly:

#(color(red)(-3) xx 2t) + (color(red)(-3) xx -4) + 2t = 4t - 3#

#-6t + 12 + 2t = 4t - 3#

We can now group and combine like terms on the left side of the equation:

#-6t + 2t + 12 = 4t - 3#

#(-6 + 2)t + 12 = 4t - 3#

#-4t + 12 = 4t - 3#

Next, add #color(red)(4t)# and #color(blue)(3)# to each side of the equation to isolate the #t# term:

#color(red)(4t) - 4t + 12 + color(blue)(3) = color(red)(4t) + 4t - 3 + color(blue)(3)#

#0 + 15 = 8t - 0#

#15 = 8t#

Now, divide each side of the equation by #color(red)(8)# to solve for #t# while keeping the equation balanced:

#15/color(red)(8) = (8t)/color(red)(8)#

#15/8 = (color(red)(cancel(color(black)(8)))t)/cancel(color(red)(8))#

#15/8 = t#

#t = 15/8#

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