Given the equation:
[tex]\sqrt[]{3x+7}=-4[/tex]Since x = 3 was obtained, let's input 3 for x in the equation to verify.
Substitute x for 3 in the equation:
[tex]\begin{gathered} \sqrt[]{3(3)+7}=-4 \\ \\ \sqrt[]{9+7}=-4 \\ \\ \sqrt[]{16}=-4 \\ \\ 4\text{ = -4} \end{gathered}[/tex]We can see that x ≠ 3
Therefore, we can say that the solution x=3 deos not satisfy the original equation.
Let's also input x= -3:
[tex]\begin{gathered} \sqrt[]{3(-3)+7}=-4 \\ \\ \sqrt[]{-9+7}=-4 \\ \\ \sqrt[]{-2}=-4 \end{gathered}[/tex]The solution x = 3 also does not satisfy the original equation.
Let's input x = -1/3
[tex]\begin{gathered} \sqrt[]{3(-\frac{1}{3})+7}=-4 \\ \\ \sqrt[]{-1+7}=-4 \\ \\ \sqrt[]{6}=-4 \end{gathered}[/tex]The solution x = -1/3 also does not satisfy the original equation.
ANSWER:
It does not satisfy the original equation
