Question

Solve 3(x – 4) = -1/2(24 – 6x)

a. X = 2
b. No solution
c. X = 12
d. Infinite solutions

Answer 1

To solve the equation, distribute the negative fraction, combine like terms, and isolate x. The equation has infinite solutions.

Step-by-step explanation:

To solve the equation 3(x – 4) = -1/2(24 – 6x), we can distribute the -1/2 to the terms inside the parentheses. Then we combine like terms and isolate x. Here are the steps:

1. Distribute -1/2 to 24 and -6x: -1/2(24) = -12 and -1/2(-6x) = 3x
2. Combine like terms: 3(x – 4) = -12 + 3x
3. Distribute 3 to x and -4: 3x - 12 = -12 + 3x
4. Combine like terms: -12 = -12

Since -12 = -12 is true, the equation has infinite solutions. Therefore, the answer is d. Infinite solutions.