To solve the equation 3/(3x) + 1/(x + 4) = 10/(7x), we need to find the value of x. Let’s break down the steps:
- Find a common denominator: The left side has two fractions, one with a denominator of 3x and the other with x + 4. The least common denominator (LCD) of the left-hand side would be 3x(x + 4). For the right side, the denominator is 7x. Therefore, the overall common denominator will be 21x(x + 4).
- Rewrite each term using the common denominator:
- For the first fraction, multiply both the numerator and the denominator by (x + 4):
(3/(3x)) * ((x + 4)/(x + 4)) = 3(x + 4)/(3x(x + 4)) - For the second fraction, multiply both the numerator and the denominator by 3x:
(1/(x + 4)) * (3x/3x) = 3x/(3x(x + 4)) - For the right side, multiply both the numerator and the denominator by 3(x + 4):
(10/(7x)) * (3(x + 4)/(3(x + 4))) = 30(x + 4)/(21x(x + 4))
- For the first fraction, multiply both the numerator and the denominator by (x + 4):
- Combine the fractions on the left side:
The left side can now be written as:
(3(x + 4) + 3x) / (21x(x + 4)) = 30(x + 4)/(21x(x + 4)) - Eliminate the denominators: Since both sides of the equation are fractions with the same denominators, we can set the numerators equal to each other:
3(x + 4) + 3x = 30(x + 4) - Simplify the equation:
1. Expand the left side:
3x + 12 + 3x = 30x + 120
6x + 12 = 30x + 120 - 2. Rearrange to isolate x:
6x – 30x = 120 – 12
-24x = 108 - 3. Solve for x:
x = -108/24
x = -4.5
Thus, the solution to the equation 3/(3x) + 1/(x + 4) = 10/(7x) is x = -4.5.