Final answer:
To solve the equation (x/12) = 2(x/14) - 32, you multiply both sides by the least common multiple of the denominators, simplify, and then solve for x, which results in approximately 158.12.
Step-by-step explanation:
We need to find the value of x in the equation (x/12) = 2(x/14) - 32.
First, let's clear the fractions by multiplying the entire equation by the least common multiple of the denominators, which is 84. We get:
7x = 12(2x) - 2688
Simplify and collect like terms:
7x = 24x - 2688
Subtract 24x from both sides:
-17x = -2688
Now, divide both sides by -17 to solve for x:
x = 2688 / 17
x = 158.12 (rounded to two decimal places)
Therefore, the value of x is approximately 158.12.