Question

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

Answer 1

`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`

Answer 2

`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"`