What is the value of x in the equation Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
To solve the equation, we will need to follow the order of operations (PEMDAS).
Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth
First, we simplify within the parentheses:
One-fourth x + 8 = 4x/4 + 8 = (x + 32)/4
One-half x + 2 = 2x/2 + 2 = (x + 4)/2
So the equation becomes:
(3/4)(x + 32)/4 - (x + 4)/2 = 3/8(4 - x) - 1/4
Now, we multiply both sides of the equation by 4 to eliminate the denominators:
3(x + 32)/4 - 2(x + 4)/2 = 3(4 - x)/8 - 4/4
Canceling out the denominators and simplifying further:
3(x + 32) - 4(x + 4) = 3(4 - x) - 4
3x + 96 - 4x - 16 = 12 - 3x - 4
Simplifying the equation, we have:
-x + 80 = 12 - 3x - 4
Combining like terms:
-x + 80 = 8 - 3x
Now, we add 3x to both sides of the equation:
2x + 80 = 8
Next, we subtract 80 from both sides of the equation:
2x = -72
Finally, we divide both sides of the equation by 2 to solve for x:
x = -36
Therefore, the value of x in the equation is -36.