Question

Explain why you do not need to do any algebra to know that the equation 3√x+7 = -4 has no solutions.

Answer 1

If you mean

`3√(x)+7=-4`

You can subtract 7 from both sides and divide both sides by 3:

`√(x) = -(-11)/(3)`

If you mean

`3√(x+7)=-4`

You can divide both sides by 3:

`√(x+7) = -(-4)/(3)`

In both cases, you're asking that the square root of something is negative, and this is not possible.