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?

Answer 1

Explanation:

Given

Required

Solve for x

Open all brackets

Collect like terms

Solve fraction

Multiply both sides by 6

Answer 2

`x =-24`

Explanation:

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 all brackets

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

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

Solve fraction

`(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`