How do you solve -3v - \frac { 5} { 2} = \frac { 7} { 2} v - \frac { 4} { 3}?

1 Answer
Jun 22, 2017

v=23/39

Explanation:

First, get rid of the fractions by multiplying everything by a number which a multiple of both 2 and 3, say 6:

color(red)(6)xx(-3v-5/2)=color(red)(6)xx(7/2v-4/3)

Distribute the 6 through the parentheses on both sides

6xx(-3v)-6xx(5/2)=6xx(7/2v)-6xx(4/3)

-18v-3xx5=3xx7v-2xx4

-18v-15=21v-8

Add 18v to both sides

-18vcolor(red)(+18v)-15=21vcolor(red)(+18v)-8

15=39v-8

Add 8 to both sides, to the variable v "more alone"

15color(red)(+8)=39v-8color(red)(+8)

23=39v

Divide both sides by 39 to isolate the v

23/color(red)(39)=(cancel(39)v)/color(red)(cancel(39))

This leaves

v=23/39

Because 23 is a prime number, this fraction is reduced to lowest terms.