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

Answer 1

Interpreting the first equation as (2/3)((1/2)x + 12) = (1/2)((1/3)x + 14) − 3:

(2/3)((1/2)x + 12) = (1/3)x + 8
(1/2)((1/3)x + 14) − 3 = (1/6)x + 4

So (1/3)x + 8 = (1/6)x + 4
(1/3 − 1/6)x = −4 → (1/6)x = −4 → x = −24.

The other equation (1/2)(n − 4) − 3 = 3 − (2n + 3) gives
(1/2)n − 5 = −2n → (5/2)n = 5 → n = 2.

Answers: x = −24 (and n = 2).