Final answer:
To solve for x in the equation 9 = (2x - 40)/(x + 10), we multiply both sides by (x + 10) and simplify to get 7x = -130. Then, divide by 7 to find x ≈ -18.5714. This solution can be justified with proper algebraic rearrangement and by rechecking the solution.
Step-by-step explanation:
To find the value of x in the equation 9 = (2x - 40)/(x + 10), we need to perform some algebraic manipulations. Let's start by multiplying both sides of the equation by (x + 10) to get rid of the denominator:
9(x + 10) = 2x - 40
Expanding the left side of the equation, we have:
9x + 90 = 2x - 40
Now, let's move all terms involving x to one side and constants to the other side:
9x - 2x = -40 - 90
7x = -130
To isolate x, we divide both sides by 7:
x = -130 / 7
x ≈ -18.5714
The value of x in the equation is approximately -18.5714. We justify this solution by ensuring that the steps of our algebraic rearrangement are mathematically valid and by checking the solution against the original equation.