Question #92f49

2 Answers
Sep 15, 2017

#1 13/84# or #97/84#

Explanation:

#x-7/12=4/7#
First, we add #7/12# to both sides, so instead of the equation being #x-7/12#, we can make it just #x#.
So when you add #7/12# to both sides, it will look like this.
#x-7/12color(blue)+color(blue)7color(blue)/color(blue)12=4/7color(blue)+color(blue)7color(blue)/color(blue)12#
That means
#x=4/7+7/12#.
To do #4/7+7/12# We find the least common denominator.
#7*12=84#
Then we adjust fractions based on the least common denominator (84).

#(4*12)/84+(7*7)/84#

Since the denominators are equal, combine the fractions.

#(4*12+7*7)/84#

#4*12=48# and #7*7=49#
#49+48=97#
Ans: #97/84

To change to a mixed number.
97 has one group of 84 and 13 remaining so it will be #1 13/84#.

Ans: #97/84# or #1 13/84#.

Sep 17, 2017

If you meant: #(x-7)/12=-4/7,# #x=1/7#

If you meant: #x-7/12=-4/7,##x=1/84#

Explanation:

#color(green)"If you meant":# #(x-7)/12=-4/7#.

Solve:

#(x-7)/12=-4/7#

Multiply both sides of the equation by #12#.

#12xx(x-7)/12=-4/7xx12#

Simplify.

#color(red)cancel(color(black)(12))^1xx(x-7)/color(red)cancel(color(black)(12))^1=-4/7xx12#

#x-7=-48/7#

Add #7# to both sides of the equation.

#x-7+7=-48/7+7#

Simplify.

#x=-48/7+7#

For any whole number, #n=n/1#.

Rewrite the equation.

#x=-48/7+7/1#

In order to add or subtract fractions, they must have the same denominator, called the least common denominator, or LCD. We can multiply the denominators to get #7# as the LCD. Now we need to multiply #7/1# by a fraction equal to #1# that will give it the denominator #7#. An example is #5/5=1#.

#x=-48/7+7/1xxcolor(red)7/color(red)7#

Simplify.

#x=-48/7+49/7#

#x=1/7#

#color(blue)"If you meant:" color(white)(.) x-7/12=-4/7#.

Solve:

#x-7/12=-4/7#

Add #7/12# to both sides.

#x-7/12+7/12=-4/7+7/12#

Simplify.

#x=-4/7+7/12#

We need to find a common denominator in order to add the fractions. Multiply the denominators #7# and #12# to get #84#. Now multiply both fractions by a fraction that equals #1# and makes the denominator #84#. For example, #9/9=1#. This way the value of the fraction does not change, it just changes in appearance.

#x=-4/7xx12/12+7/12xx7/7#

Simplify.

#x=-48/84+49/84#

#x=(-48+49)/84#

#x=1/84#