The given equation:
[tex]|x+3|+7=2[/tex]can be simplified as follow
Step 1: collect like terms
[tex]\begin{gathered} |x+3|=2-7 \\ |x+3|=-5 \end{gathered}[/tex]Step 2: Sice the equation involves absolute values,
assume two cases
case 1: take the result of the left-hand side to be positive so that
[tex]x+3=-5[/tex]Then
[tex]\begin{gathered} x=-5-3 \\ x=-8 \end{gathered}[/tex]Case 2: take the result of the left-hand side to be negative so that
[tex]\begin{gathered} x+3=-(-5) \\ x+3=5 \end{gathered}[/tex]then
[tex]\begin{gathered} x=5-3 \\ x=2 \end{gathered}[/tex]Step 3: Check if the values of x obtained in step 2 satisfy the original equation
when x=-8
[tex]\begin{gathered} |x+3+7=2 \\ |-8+3|+7 \\ |-5|+7=5+7 \\ \sin ce \\ 5+7\ne2 \\ i\mathrm{}e \\ 12\ne2 \end{gathered}[/tex]Then x=-8 is not a solution
Similarly
when x=2
[tex]\begin{gathered} |x+3|+7=2 \\ |2+3|+7=|5|+7 \\ 5+7\ne2 \\ i\mathrm{}e \\ 12\ne2 \end{gathered}[/tex]Also, x=2 is not a solution,
therefore
The equation has no solution
