Solve the equation by first clearing the fractions.
1/7 (x - 14) + 1/4 (x + 4) = x + 6
To clear the fractions, we can multiply every term in the equation by the least common denominator (LCD) of the fractions. In this case, the LCD is 28 because it's the least common multiple of 7 and 4.
Multiplying both sides of the equation by 28 gives us:
28 * (1/7) * (x - 14) + 28 * (1/4) * (x + 4) = 28 * (x + 6)
The fractions cancel out on the left side of the equation:
4(x - 14) + 7(x + 4) = 28(x + 6)
Now we distribute and simplify:
4x - 56 + 7x + 28 = 28x + 168
Combine like terms:
11x - 28 = 28x + 168
Subtract 11x from both sides:
-28 = 17x + 168
Subtract 168 from both sides:
-196 = 17x
Divide by 17:
x = -196 / 17