Question

How do you solve \[v+\dfrac{9}{3}=8\]?

Answer 1

Hint: An equation can be solved by taking all the constants on one side and unknowns to the other side. The constant side must be solved step-by-step to get through the solution. We need to do the addition, subtraction, multiplication, and division operations in such a way to simplify the equation.
As per the given question, we are provided with an equation to find its solution. We call it the solution of a given equation, which when substituted back into the equation, both sides will be equal. And the given equation is \[v+\dfrac{9}{3}=8\].

Complete step by step answer:
We have a fraction in the given equation. So, firstly, we have to express all the constant terms into their fraction forms. Then, we get
\[\Rightarrow v+\dfrac{9}{3}=\dfrac{8}{1}\]
Now, we have to take all the constant terms to one side of the equation and the unknown variable to the other side. We know that, shifting a positive number from one side of the equation to the other side, it becomes negative and vice versa. Then, we get
\[\Rightarrow v=\dfrac{8}{1}-\dfrac{9}{3}\]
Denominator of \[\dfrac{8}{1}\] is 1 and that of \[\dfrac{9}{3}\] is 3. So, we have to multiply the numerator and denominator of \[\dfrac{8}{1}\] with 3. Then, we get
\[\Rightarrow v=\dfrac{8\times 3}{1\times 3}-\dfrac{9}{3}\]
On multiplying 8 with 3 and 1 with 3, we get 24 and 3 respectively. By substituting these values in the previous equation, we get
\[\Rightarrow v=\dfrac{24}{3}-\dfrac{9}{3}\]
Here, the denominators of both the fractions are the same. So, we can directly solve the numerators. Hence, we can write as
\[\Rightarrow v=\dfrac{24-9}{3}\]
On subtracting 9 from 24, we get 15. Then, the equation becomes
\[\Rightarrow v=\dfrac{15}{3}\]
Finally, by dividing 15 by 3, we get 5 as the solution. That is, \[\Rightarrow v=5\].
\[\therefore v=5\] is the solution to the equation \[v+\dfrac{9}{3}=8\].

Note:
 We can rather solve the given equation by simply dividing 9 by 3 and then subtracting it from 8, which gives the solution. This is a two-step solution that involves just two steps towards the solution. We must avoid calculation mistakes to get the correct results.