Answer
x = 1
Work Step by Step
$\frac{2}{3}$ + $\frac{x}{4}$ = $\frac{5}{12}$ + $\frac{x}{2}$
Multiply both sides by the LCD (least common denominator), which is 12:
12($\frac{2}{3}$ + $\frac{x}{4}$) = 12($\frac{5}{12}$ + $\frac{x}{2}$)
12($\frac{2}{3}$) + 12($\frac{x}{4}$) = 12($\frac{5}{12}$) + 12($\frac{x}{2}$)
Now, cancel out the denominators:
12($\frac{2}{3}$) + 12($\frac{x}{4}$) = 12($\frac{5}{12}$) + 12($\frac{x}{2}$) --> 4(2) + 3x = 5 + 6x --> 8 + 3x = 5 + 6x
Now, combine like terms:
8 + 3x - 8 = 5 + 6x - 8 --> 3x = -3 + 6x
3x - 6x = -3 + 6x -6x
-3x = -3
Divide both sides by -3 to get x by itself:
-3x $\div$ -3 = -3 $\div$ -3
x = 1
