# How do you solve #\frac { 2} { 3} x - 5= \frac { x } { 4} - 10#?

##### 2 Answers

#### Explanation:

Let's solve this one step at a time.

First, we need to get rid of the pesky fractions. Since there are 2 fractions, let's find the LCM (Lowest common multiple). Both 3 and 4 goes in 12, so let's multiply the equation by 12.

Therefore,

To get

Subtract

Finally, divide both sides by 5 to isolate

#### Explanation:

#"collect terms in x on the left side and numeric values on the"#

#"right side"#

#"Note " 2/3x=(2x)/3#

#"subtract " x/4" from both sides"#

#rArr(2x)/3-x/4-5=cancel(x/4)cancel(-x/4)-10#

#"add 5 to both sides"#

#(2x)/3-x/4cancel(-5)cancel(+5)=-10+5#

#rArr(2x)/3-x/4=-5#

#"before subtracting the fractions we require them to"#

#"have a "color(blue)"common denominator"#

#" the lowest common multiple of 3 and 4 is 12"#

#rArr(2x)/3xx4/4-x/4xx3/3=-5#

#rArr(8x)/12-(3x)/12=-5#

#rArr(5x)/12=-5#

#"multiply both sides by 12"#

#cancel(12)xx(5x)/cancel(12)=(-5xx12)#

#rArr5x=-60#

#"divide both sides by 5"#

#(cancel(5) x)/cancel(5)=(-60)/5#

#rArrx=-12#

#color(blue)"As a check"# Substitute this value into the equation and if both sides are equal then it is the solution.

#"left side "=(2/3xx-12)-5=-8-5=-13#

#"right side "=(-12)/4-10=-3-10=-13#

#rArrx=-12" is the solution"#