Question

What is the value of x in the equation ?

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.
StartFraction one-half EndFraction left-parenthesis n minus 4 right-parenthesis minus 3 equals 3 minus left-parenthesis 2 n plus 3 right-parenthesis.
2
13

Answer 1

The text contains two equations. Solving each:

1) (2/3)((1/2)x + 12) = (1/2)((1/3)x + 14) − 3
- Left: (2/3)(1/2)x + (2/3)·12 = (1/3)x + 8
- Right: (1/2)(1/3)x + (1/2)·14 − 3 = (1/6)x + 4
So (1/3)x + 8 = (1/6)x + 4
(1/3 − 1/6)x = 4 − 8 → (1/6)x = −4 → x = −24

2) (1/2)(n − 4) − 3 = 3 − (2n + 3)
- Left: (1/2)n − 2 − 3 = (1/2)n − 5
- Right: 3 − 2n − 3 = −2n
So (1/2)n − 5 = −2n → (5/2)n = 5 → n = 2

Answers: x = −24 and n = 2.