In this problem, we have the following equation:
[tex]2a+b=2a[/tex]
And the problem states that [tex]a[/tex] and [tex]b[/tex] are nonzero real numbers. First of all, we need to assume that [tex]a[/tex] and [tex]b[/tex] are nonzero real numbers. Thus, let's say that:
[tex]a=1 \\ \\ b=1[/tex]
Plug in the equation, we have:
[tex]2(1)+(1)=2(1) \\ \\ 2+1=2 \\ \\ 3=2 \ Absurd![/tex]
As you can see, we got an absurd statement since [tex]3\neq 2[/tex]. Then, the only possible solution is that [tex]b=0[/tex]. So, we can write our equation as follows:
[tex]2a+b=2a \\ \\ 2a+(0)=2a \\ \\ 2a=2a \ True![/tex]
Conclusion:
For any real number [tex]a[/tex], we will have that [tex]b=0[/tex]
