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

2 Answers
May 17, 2018

Answer:

#x = -11#

Explanation:

Simplify to remove fractions.

#1/2(x-3) = 1/3(2x+1)#

Multiply by 6 through out:

#6 xx 1/2(x-3) = 6 xx 1/3(2x+1)#

#3(x-3) = 2(2x+1)#

#3x-9 = 4x + 2#

#3x-4x = 2 + 9#

#-x = 11#

#x = -11#

Check the answer:

#1/2(-11-3) = 1/3(2xx(-11) + 1)#
#1/2 xx -14 = 1/3(-22 +1)#
#-7 = 1/3xx(-21)#
#-7 = -7#

May 17, 2018

Answer:

#x=-11#

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"#