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$-\frac{5}{x}-5=-\frac{10}{x}-.6$

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Add and subtract rational numbers

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Q.

-\frac{5}{x}-5=-\frac{10}{x}-.6

Set up equation: Set up the equation. $\newline$ $-\frac{5}{(x-5)} = -\frac{10}{(x-0.6)}$ $\newline$ We have a proportion here, where two ratios are set equal to each other. We can solve for $x$ by cross-multiplying.
Cross-multiply: Cross-multiply to find an equation without fractions. $\newline$ $-5 \times (x - 0.6) = -10 \times (x - 5)$ $\newline$ This will give us a linear equation that we can solve for $x$ .
Distribute numbers: Distribute the numbers on both sides. $\newline$ $-5x + 3 = -10x + 50$ $\newline$ We have distributed $-5$ into $(x - 0.6)$ and $-10$ into $(x - 5)$ .
Combine like terms: Add $10x$ to both sides to get all $x$ terms on one side. $\newline$ $-5x + 10x + 3 = -10x + 10x + 50$ $\newline$ $5x + 3 = 50$ $\newline$ We have combined like terms on both sides of the equation.
Isolate $x$ term: Subtract $3$ from both sides to solve for $x$ . $\newline$ $5x + 3 - 3 = 50 - 3$ $\newline$ $5x = 47$ $\newline$ We have isolated the $x$ term on one side of the equation.
Find value of x: Divide both sides by $5$ to find the value of $x$ . $\frac{5x}{5} = \frac{47}{5}$ $x = \frac{47}{5}$ $x = 9.4$ We have found the value of $x$ .

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