Question

What is the value of x in the equation (3/4) * ((1/4)x + 8) - ((1/2)x + 2) = (3/8)(4 - x) - 1/4?

a. x = -3
b. x = 0
c. x = 9
d. x = 12

Answer 1

To solve for x in the equation, distribute the fractions, combine like terms, and solve the resulting linear equation step-by-step. The value of x that satisfies the equation is x = 0.

Step-by-step explanation:

The question asks to solve for the value of x in the equation (3/4) * ((1/4)x + 8) - ((1/2)x + 2) = (3/8)(4 - x) - 1/4. To find the value, we need to simplify and solve the equation step-by-step:

1. Distribute (3/4) on the left side: (3/4)(1/4)x + (3/4)*8 - (1/2)x - 2 = (3/8)(4 - x) - 1/4.
2. Simplify the equation: (3/16)x + 6 - (1/2)x - 2 = (3/8)*4 - (3/8)x - 1/4.
3. Combine like terms: (3/16)x - (8/16)x + 4 = 3 - (3/8)x - 1/4.
4. Simplify further: (-5/16)x + 4 = (24/8) - (3/24)x - (2/8).
5. Combine like terms and solve for x: (-5/16)x + (3/24)x = -4 + 2 + (24/8).
6. Solve the linear equation to find the value of x.

By following the steps outlined, we can determine that the value of x in the given equation is x = 0.