Final answer:
To solve the equation 3x - 8 = 1/2(8x + 4), we first eliminate the fraction by multiplying both sides by 2, rearrange the equation to get all x terms on one side, and then solve for x to find that x equals √10.
Step-by-step explanation:
The equation provided by the student is 3x − 8 = ½(8x+4). To solve for x, we need to clear the fraction by multiplying both sides of the equation by 2, then simplifying and solving for x.
- Multiply both sides by 2 to eliminate the fraction: 2(3x-8) = (8x+4)
- Distribute the 2 on the left side: 6x - 16 = 8x + 4
- Move all x terms to one side and constant terms to the opposite side: -16 - 4 = 8x - 6x
- Combine like terms: -20 = 2x
- Divide by 2 to solve for x: x = √10
Thus, the value of x is √10.