To solve the equation 3/(3x) + 1/(x + 4) = 10/(7x), we start by finding a common denominator for all the fractions involved. The denominators are 3x, x + 4, and 7x. The least common multiple of these three expressions is 21x(x + 4).
Next, we will multiply every term in the equation by this common denominator to eliminate the fractions:
- Multiplying the first term:
3/(3x) * 21x(x + 4) = 21(x + 4) - Multiplying the second term:
1/(x + 4) * 21x(x + 4) = 21x - Multiplying the third term:
10/(7x) * 21x(x + 4) = 30(x + 4)
So, we have:
21(x + 4) + 21x = 30(x + 4)
Expanding both sides, we get:
21x + 84 + 21x = 30x + 120
Combining like terms results in:
42x + 84 = 30x + 120
Now, we will isolate the variable x. Subtract 30x from both sides:
12x + 84 = 120
Next, subtract 84 from both sides:
12x = 36
Finally, divide both sides by 12 to solve for x:
x = 3
In conclusion, the solution to the equation 3/(3x) + 1/(x + 4) = 10/(7x) is x = 3.