To solve the exercise, set both expressions equal and then solve for x, like this
[tex]\begin{gathered} 4x+3=-x-2 \\ \text{ Subtract 3 from both sides of the equation} \\ 4x+3-3=-x-2-3 \\ 4x=-x-5 \\ \text{ Add x from both sides of the equation} \\ 4x+x=-x-5+x \\ 5x=-5 \\ \text{ Divide by 5 into both sides of the equation} \\ \frac{5x}{5}=\frac{-5}{5} \\ x=-1 \end{gathered}[/tex]Therefore, the value of x that makes the given expressions have the same value is
[tex]x=-1[/tex]Checking
[tex]\begin{gathered} 4x+3=-x-2 \\ 4(-1)+3=-(-1)-2 \\ -4+3=1-2 \\ -1=-1 \end{gathered}[/tex]