Question

Solve the expression: (4x + 3)/4 - [(x - (2x - 1)/3] = x + 1/3.

A) x = 1
B) x = 2
C) x = 3
D) x = 4

Answer 1

By simplifying the given equation, we find that the value of x must equal -31/4. However, this solution is not listed in the provided options, indicating there might be a mistake in the initial problem or the answer choices.

Step-by-step explanation:

To solve the expression (4x + 3)/4 - [(x - (2x - 1)/3)] = x + 1/3, we need to simplify and solve for x. First, distribute the negative sign through the brackets and simplify the fractions:

1. Multiply everything by the least common denominator, which is 12, to eliminate the fractions:
   12 * (4x + 3)/4 - 12 * (x - (2x - 1)/3) = 12 * (x + 1/3)
2. Simplify the equation:
   3(4x + 3) - 4(x - (2x/3) + 1/3) = 4x + 4/3
3. Distribute and combine like terms:
   12x + 9 - (4x - (8x/3) - 4/3) = 4x + 4/3
4. Combine like terms and move all x terms to one side and constants to the other:
   (12x + 9 - 4x + (8x/3) + 4/3) - 4x - 4/3 = 0
5. Combine like terms and solve for x:
   12x - 4x + 8x/3 - 4x = -9 - 4/3
   (24x - 12x + 8x - 12x)/3 = -27/3 - 4/3
   (8x - 4x)/3 = -31/3
   4x/3 = -31/3
   x = -31/4
6. Through these steps, we find that x must equal -31/4, which is not one of the provided options A) x = 1, B) x = 2, C) x = 3, or D) x = 4. There could be an error in the original equation or in the provided options.