Question

What is the value of x in the equation (StartFraction one-half EndFractionx + 12) = StartFraction one-half EndFraction(StartFraction 2 Over 3 EndFraction left-parenthesis StartFraction one-half EndFraction. x plus 12 right-parenthesis equals left-parenthesis StartFraction one-half EndFraction left-parenthesis StartFraction one-third EndFraction x plus 14 right-parenthesis minus 3.x + 14) – 3?

–24
–6
negative StartFraction 2 Over 3 EndFraction.
0

Answer 1

Answer: option A. -24

Explanation:

Answer 2

`x = -24`

Explanation:

Your question is not well presented

Given

`(2)/(3)((1)/(2)x + 12) = (1)/(2)((1)/(3)x + 14) - 3`

Required

Solve for x

`(2)/(3)((1)/(2)x + 12) = (1)/(2)((1)/(3)x + 14) - 3`

Open Brackets

`(2)/(3)*(1)/(2)x + (2)/(3)*12 = (1)/(2)*(1)/(3)x +(1)/(2)* 14 - 3`

`(1)/(3)x + (2*12)/(3) = (1)/(6)x +(14)/(2) - 3`

`(1)/(3)x + (24)/(3) = (1)/(6)x +(14)/(2) - 3`

`(1)/(3)x + 8 = (1)/(6)x +7 - 3`

Collect Like Terms

`(1)/(3)x - (1)/(6)x= 7 - 3 - 8`

`(1)/(3)x - (1)/(6)x= -4`

Take LCM

`(2-1)/(6)x= -4`

`(1)/(6)x= -4`

Multiply both sides by 6

`6*(1)/(6)x= -4*6`

`x= -4*6`

`x = -24`