# How do you solve the linear equation #1/2 (x-3) = 1/3 (2x+1)#?

##### 2 Answers

#### Answer:

#### Explanation:

Simplify to remove fractions.

Multiply by 6 through out:

Check the answer:

#### Answer:

#### Explanation:

#"eliminate the fractions by multiplying both sides by"#

#"the "color(blue)"lowest common multiple of 2 and 3"#

#"the lowest common multiple of 2 and 3 is 6"#

#rArrcancel(6)^3xx1/cancel(2)^1(x-3)=cancel(6)^2xx1/cancel(3)^1(2x+1)#

#rArr3(x-3)=2(2x+1)larrcolor(blue)"no fractions"#

#"distribute brackets on both sides"#

#3x-9=4x+2#

#"subtract "3x" from both sides"#

#rArr-9=x+2#

#"subtract 2 from both sides"#

#rArr-11=xrArrx=-11#

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

#"left "=1/2(-14)=-7#

#"right "=1/3(-21)=-7#

#rArrx=-11" is the solution"#