Solving the Equation: 3/4(1/4 x+8) - (1/2x+2) = 3/8(4-x) - 1/4x
In this article, we will solve the equation 3/4(1/4 x+8) - (1/2x+2) = 3/8(4-x) - 1/4x step by step.
Step 1: Simplify the Left Side of the Equation
The left side of the equation is 3/4(1/4 x+8) - (1/2x+2). Let's simplify it:
3/4(1/4 x+8) = 3/4(1/4 x) + 3/4(8) = 3/16 x + 6
Now, subtract (1/2x+2) from 3/16 x + 6:
3/16 x + 6 - 1/2x - 2 = 3/16 x - 4/8x - 2 + 6 (convert 1/2x to 4/8x) = -1/16x + 4 (combine like terms)
So, the simplified left side of the equation is -1/16x + 4.
Step 2: Simplify the Right Side of the Equation
The right side of the equation is 3/8(4-x) - 1/4x. Let's simplify it:
3/8(4-x) = 3/8(4) - 3/8x = 3/2 - 3/8x
Now, subtract 1/4x from 3/2 - 3/8x:
3/2 - 3/8x - 1/4x = 3/2 - 5/8x (combine like terms)
So, the simplified right side of the equation is 3/2 - 5/8x.
Step 3: Equate the Two Expressions
Now that we have simplified both sides of the equation, we can equate them:
-1/16x + 4 = 3/2 - 5/8x
Step 4: Solve for x
Let's add 1/16x to both sides of the equation to get:
4 = 3/2 - 9/16x
Now, add 9/16x to both sides of the equation to get:
4 + 9/16x = 3/2
Subtract 4 from both sides of the equation to get:
9/16x = -1/2
Multiply both sides of the equation by 16 to get:
9x = -8
Divide both sides of the equation by -9 to get:
x = 8/9
Therefore, the value of x is 8/9.
