# How do you solve #x+ \frac { 5} { 6} = 2x - \frac { 1} { 4}#?

##### 1 Answer

Apr 27, 2018

#### Explanation:

#"We can eliminate the fractions in the equation by"#

#"multiplying all terms by the "color(blue)"lowest common multiple"#

#"of 6 and 4, that is 12"#

#12x+(cancel(12)^2xx5/cancel(6)^1)=24x-(cancel(12)^3xx1/cancel(4)^1)#

#rArr12x+10=24x-3larrcolor(red)"no fractions"#

#"collect terms in x on one side of the equation and numeric"#

#"values on the other side"#

#"subtract "12x" from both sides"#

#cancel(12x)cancel(-12x)+10=24x-12x-3#

#rArr10=12x-3#

#"add 3 to both sides"#

#10+3=12xcancel(-3)cancel(+3)#

#rArr13=12x#

#"divide both sides by 12"#

#13/12=(cancel(12) x)/cancel(12)#

#rArrx=13/12#