Question

How do you solve $10x=8$?

Answer 1

Hint: We solve the given linear equation by simplifying the equation. We divide both sides of the equation $10x=8$ with 10. Then we simplify the right-hand side fraction to get the solution for $x$. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form when the G.C.D is 1.

Complete step by step answer:
The given equation $10x=8$ is a linear equation of $x$.
We divide both sides of the equation $10x=8$ with 10.
\[\begin{align}
  & \dfrac{10x}{10}=\dfrac{8}{10} \\
 & \Rightarrow x=\dfrac{8}{10} \\
\end{align}\]
We need to find the simplified form of the proper fraction $\dfrac{8}{10}$.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 1.
For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.
For our given fraction $\dfrac{8}{10}$, the G.C.D of the denominator and the numerator is 2.
$\begin{align}
  & 2\left| \!{\underline {\,
  8,10 \,}} \right. \\
 & 1\left| \!{\underline {\,
  4,5 \,}} \right. \\
\end{align}$
Now we divide both the denominator and the numerator with 2 and get $\dfrac{{}^{8}/{}_{2}}{{}^{10}/{}_{2}}=\dfrac{4}{5}$.
Therefore, the simplified form of $\dfrac{8}{10}$ is $\dfrac{4}{5}$.

Note:
The process of simplification comes from the G.C.D of the denominator and the numerator. In the case of linear equations, the number of solutions in every case will be 1. The simplified form will be equal to the value of $x$.