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Find the value of x in the equation 9 = (2x - 40)/(x + 10). Justify your equation.

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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.

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