How do you solve #7= 12+ \frac { 1} { 2} a#?

2 Answers
Aug 22, 2017

# a = -10#

Explanation:

#7 = 12 + 1/2a#

#7 = 12 + a/2#

Multiply through with the LCM

# 7 xx 2 = 12 xx 2 + a/2 xx 2#

# 14 = 24 + a/cancel2 xx cancel2#

# 14 = 24 + a#

Collect like terms

# a = 14 - 24#

# a = -10#

Aug 22, 2017

See a solution process below:

Explanation:

First, subtract #color(red)(12)# from each side of the equation to isolate the #a# term while keeping the equation balanced:

#-color(red)(12) + 7 = -color(red)(12) + 12 + 1/2a#

#-5 = 0 + 1/2a#

#-5 = 1/2a#

Now, multiply each side of the equation to by #color(red)(2)# to solve for #a# while keeping the equation balanced:

#color(red)(2) xx -5 = color(red)(2) xx 1/2a#

#-10 = cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))a#

#-10 = 1a#

#-10 = a#

#a = -10#