8/x+4 = 12/5x - 13 (solve the proportion)
The way you typed it ....
multiply each term by 5x the LCD
8 + 4x = 12x^2 - 13x
12x^2 - 17x - 8 = 0
use the quadratic formula to find 2 answers
what you probably meant:
8/(x+4) = 12/(5x-13)
40x - 104 = 12x + 48
28x = 152
x = 152/28 = 38/7
152
To solve this proportion, we need to isolate the variable x. Here's how you can do it:
Step 1: Get rid of the denominators by multiplying both sides of the equation by the lowest common denominator (LCD) of 5x:
5x * (8/x + 4) = 5x * (12/5x - 13)
This simplifies to:
40 + 20x = 12 - 65x
Step 2: Group the x terms on one side of the equation and the constant terms on the other side:
20x + 65x = 12 - 40
This simplifies to:
85x = -28
Step 3: Solve for x by dividing both sides of the equation by 85:
x = -28/85
Therefore, the solution to the proportion is:
x ≈ -0.3294 (rounded to four decimal places)
You can verify the answer by substituting this value back into the original equation to ensure it satisfies the equation.