# Solve for: (10)/(x+8)=(160)/(108)

## Expression: $\frac{ 10 }{ x+8 }=\frac{ 160 }{ 108 }$

Determine the defined range

$\begin{array} { l }\frac{ 10 }{ x+8 }=\frac{ 160 }{ 108 },& x≠-8\end{array}$

Cancel out the common factor $4$

$\frac{ 10 }{ x+8 }=\frac{ 40 }{ 27 }$

Simplify the equation using cross-multiplication

$270=40\left( x+8 \right)$

Distribute $40$ through the parentheses

$270=40x+320$

Move the variable to the left-hand side and change its sign

$270-40x=320$

Move the constant to the right-hand side and change its sign

$-40x=320-270$

Subtract the numbers

$-40x=50$

Divide both sides of the equation by $-40$

$\begin{array} { l }x=-\frac{ 5 }{ 4 },& x≠-8\end{array}$

Check if the solution is in the defined range

\begin{align*}&x=-\frac{ 5 }{ 4 } \\&\begin{array} { l }x=-1 \frac{ 1 }{ 4 },& x=-1.25\end{array}\end{align*}

Random Posts
Random Articles