Question

How many solutions does the equation have? a+5=1/5(15+5a)

Answer 1

Given equation:

$a+5= \frac{1}{5} (15+5a)$.

When we get any fraction in an equation, it would better to get rid that denominator by multiplying whole equation by the number in numerator.

We have fraction 1/5 on rigth side. So, we have 5 in denominator.

Multiplying whole equation by 5 on both sides, we get

$5*(a+5)=5* \frac{1}{5} (15+5a)$

Distributing 5 on left side,

$5a+25 = 15+5a.$                          (5 * 1/5 =1  on right side)

Subtracting both sides 5a

5a+25-5a = 15+5a-5a.

25 ≠ 15.

We get 25 on left side and 15 on rigth side.

25 can't be equal to 15.

So, 25=15 is a false statement and we could say " No soutions" for the given equation.

Therefore option C is correct.

C.no solution