In order to check if x = -7 is the solution of the equation, let's use this value in the equation and check if the final sentence is true:
[tex]\begin{gathered} 2x+10=-4 \\ 2\cdot(-7)+10=-4 \\ -14+10=-4 \\ -4=-4 \end{gathered}[/tex]The final sentence is true, so the value x = -7 is the solution of the equation.