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coldgirl [10]
3 years ago
12

What is the value of x in the equation (StartFraction one-half EndFractionx + 12) = StartFraction one-half EndFraction(StartFrac

tion 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?
Mathematics
1 answer:
anastassius [24]3 years ago
8 0

Answer:

x =-24

Step-by-step explanation:

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 all 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{2 * 1}{3 *2}x + \frac{2 * 12}{3}= \frac{1 * 1}{2 * 3}x + \frac{1 * 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

Solve fraction

\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

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