Solving the Equation: 3/4(1/4x + 8) - (1/2x + 2) = 3/8(4-x) - 1/4x
In this article, we will solve the equation 3/4(1/4x + 8) - (1/2x + 2) = 3/8(4-x) - 1/4x. This equation involves fractions and variables, and we will use algebraic manipulations to solve for x.
Step 1: Simplify the Left-Hand Side
Let's start by simplifying the left-hand side of the equation:
3/4(1/4x + 8) - (1/2x + 2)
= 3/4(1/4x) + 3/4(8) - (1/2x) - 2
= 3/16x + 6 - 1/2x - 2
= (3/16 - 1/2)x + 4
Step 2: Simplify the Right-Hand Side
Next, let's simplify the right-hand side of the equation:
3/8(4-x) - 1/4x
= 3/8(4) - 3/8x - 1/4x
= 3/2 - 3/8x - 1/4x
= 3/2 - (3/8 + 1/4)x
= 3/2 - 5/8x
Step 3: Equate the Two Expressions
Now, we can equate the two expressions:
(3/16 - 1/2)x + 4 = 3/2 - 5/8x
Step 4: Solve for x
To solve for x, we can add 5/8x to both sides of the equation:
(3/16 - 1/2)x + 5/8x + 4 = 3/2
This simplifies to:
-1/16x + 4 = 3/2
Subtracting 4 from both sides gives:
-1/16x = -1/2
Multiplying both sides by -16 gives:
x = 8
Therefore, the solution to the equation is x = 8.
Conclusion
In this article, we have solved the equation 3/4(1/4x + 8) - (1/2x + 2) = 3/8(4-x) - 1/4x using algebraic manipulations. The solution to the equation is x = 8.
