Question

After solving the equation, the solution obtained was x=3. what is wrong with this solution

Answer 1

Given the equation:

`\sqrt[]{3x+7}=-4`

Since x = 3 was obtained, let's input 3 for x in the equation to verify.

Substitute x for 3 in the equation:

`\begin{gathered} \sqrt[]{3(3)+7}=-4 \\ \\ \sqrt[]{9+7}=-4 \\ \\ \sqrt[]{16}=-4 \\ \\ 4\text{ = -4} \end{gathered}`

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:

`\begin{gathered} \sqrt[]{3(-3)+7}=-4 \\ \\ \sqrt[]{-9+7}=-4 \\ \\ \sqrt[]{-2}=-4 \end{gathered}`

The solution x = 3 also does not satisfy the original equation.

Let's input x = -1/3

`\begin{gathered} \sqrt[]{3(-(1)/(3))+7}=-4 \\ \\ \sqrt[]{-1+7}=-4 \\ \\ \sqrt[]{6}=-4 \end{gathered}`

The solution x = -1/3 also does not satisfy the original equation.

ANSWER:

It does not satisfy the original equation