Repeated addition is multiplication, right?

Note that $\underbrace{2+2+2+\ldots+2}_{x \text{ times}}$ is only defined for non-negative integers $x$ . Negative numbers, decimals, fractions and irrational numbers all will cause this expression to be undefined.

You simply cannot write $2+2+2+\ldots+2$ for $10.5$ times, $-10$ times, $7\dfrac{3}{4}$ times or $\pi$ times. It's simply not possible.

If you still do not get it, consider this:

If $x=10.5, 2x=21$

$2+2+2+\ldots+2 = 21$ is simply not possible, no matter how many or how few $2$ 's you write.

Therefore,

$\underbrace{2+2+2+\ldots+2}_{x \text{ times}}=2x$

for all non-negative integers $x$ . The answer is $\boxed{\text{False}}$

Actually the LHS is incorrect. x times mean x is whole number. So this is true for whole numbers only. Other method, differentiate both the sides wrt x, you will get 0+0+0+0...+0=2. This is obviously not true. This happens because equation defined for set of whole numbers is not differentiable.