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Solve for
x.

(9)/(5)-(8)/(5x)=2
Answer:
x=

Solve for $x$ . $\newline$ $\frac{9}{5}-\frac{8}{5 x}=2$ $\newline$ Answer: $x=$

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Solve equations with the distributive property

Full solution

Q. Solve for

x

.

\newline

\frac{9}{5}-\frac{8}{5 x}=2

\newline

Answer:

x=

Combine terms: Combine the terms with $x$ on one side and the constant terms on the other side. $\newline$ To do this, we will add $\frac{8}{5}x$ to both sides of the equation. $\newline$ $\frac{9}{5} - \frac{8}{5}x + \frac{8}{5}x = 2 + \frac{8}{5}x$
Simplify equation: Simplify both sides of the equation. $\newline$ On the left side, the terms $(\frac{8}{5}x)$ cancel out, leaving us with $\frac{9}{5}$ . On the right side, we have $2 + (\frac{8}{5}x)$ . $\newline$ $\frac{9}{5} = 2 + (\frac{8}{5}x)$
Convert whole number: Convert the whole number $2$ to a fraction with the same denominator as $\frac{9}{5}$ to combine the terms. $\newline$ $2$ can be written as $\frac{10}{5}$ because $2 \times \frac{5}{5} = \frac{10}{5}$ . $\newline$ $\frac{9}{5} = \frac{10}{5} + \frac{8}{5}x$
Subtract to isolate: Subtract $(10/5)$ from both sides to isolate the term with $x$ . $\frac{9}{5} - \left(\frac{10}{5}\right) = \left(\frac{10}{5}\right) + \left(\frac{8}{5}x\right) - \left(\frac{10}{5}\right)$
Simplify equation: Simplify both sides of the equation. $\newline$ On the left side, we have $(\frac{9}{5}) - (\frac{10}{5})$ which is $(-\frac{1}{5})$ . On the right side, the $(\frac{10}{5})$ cancels out, leaving us with $(\frac{8}{5}x)$ . $\newline$ $(-\frac{1}{5}) = (\frac{8}{5}x)$
Multiply by reciprocal: Multiply both sides by the reciprocal of $(\frac{8}{5})$ to solve for $x$ . The reciprocal of $(\frac{8}{5})$ is $(\frac{5}{8})$ , so we multiply both sides by $(\frac{5}{8})$ . $(-\frac{1}{5}) \times (\frac{5}{8}) = (\frac{8}{5}x) \times (\frac{5}{8})$
Simplify result: Simplify both sides of the equation. $\newline$ On the left side, the $5s$ cancel out and we are left with $-1 \times \frac{1}{8}$ , which is $-\frac{1}{8}$ . On the right side, the $8s$ and the $5s$ cancel out, leaving us with $x$ . $\newline$ $(-\frac{1}{8}) = x$

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