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$\frac{x}{x+3} = \frac{x+2}{x+6.2}$ Find `x`

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Add and subtract rational numbers

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Q.

\frac{x}{x+3} = \frac{x+2}{x+6.2}

Find `x`

Set up equation: Set up the equation from the problem. $\newline$ We have the equation $\frac{x}{x+3} = \frac{x+2}{x+6.2}$ .
Cross-multiply: Cross-multiply to eliminate the fractions. $x \times (x + 6.2) = (x + 2) \times (x + 3)$
Distribute and simplify: Distribute to simplify both sides of the equation. $x^2 + 6.2x = x^2 + 3x + 2x + 6$
Combine like terms: Combine like terms. $x^2 + 6.2x = x^2 + 5x + 6$
Subtract $x^2$ : Subtract $x^2$ from both sides to get rid of the $x^2$ term. $\newline$ $x^2 + 6.2x - x^2 = x^2 + 5x + 6 - x^2$ $\newline$ This simplifies to: $\newline$ $6.2x = 5x + 6$
Isolate x term: Subtract $5x$ from both sides to isolate the x term. $\newline$ $6.2x - 5x = 5x + 6 - 5x$ $\newline$ This simplifies to: $\newline$ $1.2x = 6$
Solve for x: Divide both sides by $1.2$ to solve for x. $\newline$ $\frac{1.2x}{1.2} = \frac{6}{1.2}$ $\newline$ This simplifies to: $\newline$ $x = 5$

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