How do you solve the linear equation #1/2 (x-3) = 1/3 (2x+1)#?
2 Answers
Explanation:
Simplify to remove fractions.
Multiply by 6 through out:
Check the 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"#