Question

How do you simplify $\dfrac{6x-10}{-2}$?

Answer 1

Hint: We have one linear equation and one constant in the numerator and the denominator respectively. We factor the numerator taking a constant common. From them we eliminate the common factor if there is any. We find the simplified form the expression. We also find the final sign of the solution from the coefficients.

Complete step by step solution:
We have been given the division of one linear equation and one constant. We need to find the factor of the equation in the numerator. The numerator $6x-10$ is a linear equation of $x$.
The only process that is available for this equation to factorise is to take a common constant out of the terms $6x$ and $-10$.
Now we are actually taking the constant from 6 and 10. We are finding the maximum possible constant to take out. It will be the greatest common divisor of the numbers 6 and 10.
$\begin{align}
  & 2\left| \!{\underline {\,
  6,10 \,}} \right. \\
 & 1\left| \!{\underline {\,
  3,5 \,}} \right. \\
\end{align}$
Therefore, the GCD will be 2. We are taking 2 as common from the numbers 6 and 10.
Therefore, the factorisation is $6x-10=2\left( 3x-5 \right)$.
The fraction becomes $\dfrac{6x-10}{-2}=\dfrac{2\left( 3x-5 \right)}{-2}=-\left( 3x-5 \right)=5-3x$.
Therefore, the simplified form of $\dfrac{6x-10}{-2}$ is $5-3x$.

Note: We can verify the result of the simplification by taking an arbitrary value of x where $x=2$.
We put $x=2$ in the fraction form of $\dfrac{6x-10}{-2}$ and get $\dfrac{6x-10}{-2}=\dfrac{6\times 2-10}{-2}=\dfrac{2}{-2}=-1$
Now we put $x=2$ in the $5-3x$and get $5-3\times 2=5-6=-1$.
Thus, verified the simplified form of $\dfrac{6x-10}{-2}$ is $5-3x$.