Suppose you want to solve the equation 2a + b = 2a, where a and b are nonzero real numbers. Describe the solution to this equation. Justify your description.

Question

asked Oct 22, 2020 192k views

1 Answer

ElDuderino · Answer 1 · 2020-10-28T12:53:35+0000

In this problem, we have the following equation:

2a+b=2a

And the problem states that
and
are nonzero real numbers. First of all, we need to assume that
and
are nonzero real numbers. Thus, let's say that:

$a=1 \\ \\ b=1$

Plug in the equation, we have:

$2(1)+(1)=2(1) \\ \\ 2+1=2 \\ \\ 3=2 \ Absurd!$

As you can see, we got an absurd statement since
$3\\eq 2$ . Then, the only possible solution is that
b=0 . So, we can write our equation as follows:

$2a+b=2a \\ \\ 2a+(0)=2a \\ \\ 2a=2a \ True!$

Conclusion:

For any real number
, we will have that
b=0