Answer
\[x=-\frac{13}{3}\].
Work Step by Step
Consider the equation
\[2\left( x-2 \right)+3\left( x+5 \right)=2x-2\]
Apply the distributive law
\[2x-4+3x+15=2x-2\]
This gives,
\[5x+11=2x-2\]
Subtract \[2x\]from both the sides
\[3x+11=-2\]
Subtract 11 from both the sides of the above equation
\[3x=-13\]
Divide both the sides by 3
\[x=-\frac{13}{3}\]
Now, to check it, put \[x=-\frac{13}{3}\]in the equation
\[\begin{align}
& 2\left( x-2 \right)+3\left( x+5 \right)=2x-2 \\
& 2\left( -\frac{13}{3}-2 \right)+3\left( -\frac{13}{3}+5 \right)=2x-2 \\
& 2\left( -\frac{19}{3} \right)+3\left( \frac{2}{3} \right)=\frac{-26}{3}-2 \\
& \left( -\frac{38}{3} \right)+\left( \frac{6}{3} \right)=\left( \frac{-26-6}{3} \right)
\end{align}\]
Further simplifying
\[\begin{align}
& \left( -\frac{38}{3} \right)+\left( \frac{6}{3} \right)=\left( \frac{-26-6}{3} \right) \\
& \left( \frac{-38+6}{3} \right)=\left( \frac{-26-6}{3} \right) \\
& \left( \frac{-32}{3} \right)=\left( \frac{-32}{3} \right)
\end{align}\]
which is true.
Hence, the solution of the given equation is\[x=-\frac{13}{3}\].
