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

$3\sqrt{x}+7=-4$

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

$\sqrt{x} = -\dfrac{-11}{3}$

If you mean

$3\sqrt{x+7}=-4$

You can divide both sides by 3:

$\sqrt{x+7} = -\dfrac{-4}{3}$

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