Answer
\[x=3\]
Work Step by Step
Considering
\[\frac{x+5}{8}=\frac{x+2}{5}\]
The LCM of both the denominators of the above equation is 40 so multiply by 40 on both the sides of the equation
\[\begin{align}
& \frac{x+5}{8}\times 40=\frac{x+2}{5}\times 40 \\
& 5\left( x+5 \right)=8\left( x+2 \right) \\
& 5x+25=8x+16
\end{align}\]
Subtract \[8x\] from both the sides
\[-3x+25=16\]
Subtract \[25\] from both the sides
\[-3x=-9\]
Divide both the sides by \[-3\]
\[x=3\]
Now, to check it, put \[x=3\]in the equation
\[\begin{align}
& \frac{x+5}{8}=\frac{x+2}{5} \\
& \frac{3+5}{8}=\frac{3+2}{5} \\
& \frac{8}{8}=\frac{5}{5} \\
& 1=1
\end{align}\]
which is true.
Hence, required solution is\[x=3\].
