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:

$x = -24$

Step-by-step explanation:

Your question is not well presented

Given

$\frac{2}{3}(\frac{1}{2}x + 12) = \frac{1}{2}(\frac{1}{3}x + 14) - 3$

Required

Solve for x

$\frac{2}{3}(\frac{1}{2}x + 12) = \frac{1}{2}(\frac{1}{3}x + 14) - 3$

Open Brackets

$\frac{2}{3}*\frac{1}{2}x + \frac{2}{3}*12 = \frac{1}{2}*\frac{1}{3}x +\frac{1}{2}* 14 - 3$

$\frac{1}{3}x + \frac{2*12}{3} = \frac{1}{6}x +\frac{14}{2} - 3$

$\frac{1}{3}x + \frac{24}{3} = \frac{1}{6}x +\frac{14}{2} - 3$

$\frac{1}{3}x + 8 = \frac{1}{6}x +7 - 3$

Collect Like Terms

$\frac{1}{3}x - \frac{1}{6}x= 7 - 3 - 8$

$\frac{1}{3}x - \frac{1}{6}x= -4$

Take LCM

$\frac{2-1}{6}x= -4$

$\frac{1}{6}x= -4$

Multiply both sides by 6

$6*\frac{1}{6}x= -4*6$

$x= -4*6$

$x = -24$

Answer 2

Answer: option A.  -24

Step-by-step explanation: