Question

How do you solve \[14-\dfrac{1}{5}\left( j-10 \right)=\dfrac{2}{5}\left( 25+j \right)\]?

Answer 1

Hint: The given equation has a fraction on both sides of the equation, to simplify such an equation we first need to get rid of the denominator. As the highest power for the given question is one, its degree is also one, thus it is a linear equation. To solve a linear equation, we have to take all the variable terms to one side of the equation, and leave constants to the other side. By this, we can find the solution value of the equation.

Complete step by step solution:
We are given the equation \[14-\dfrac{1}{5}(j-10)=\dfrac{2}{5}(25+j)\], we have to solve it. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side. This equation has only one variable term to its one side, hence
\[14-\dfrac{1}{5}\left( j-10 \right)=\dfrac{2}{5}\left( 25+j \right)\]
To simplify the equation, we need to get rid of the fractional terms. As the denominators in both sides are the same, multiplying both sides of the above equation by 5, we get
\[\Rightarrow 5\left( 14-\dfrac{1}{5}\left( j-10 \right) \right)=5\times \dfrac{2}{5}\left( 25+j \right)\]
Simplifying both sides of the above equation, we get
\[\Rightarrow 80-j=50+2j\]
Adding j to both sides of the equation, we get
\[\Rightarrow 80=50+3j\]
 \[\begin{align}
  & \Rightarrow 3j=30 \\
 & \Rightarrow j=10 \\
\end{align}\]
Hence, the solution of the above equation is \[j=10\].

Note:
Here the denominator on both sides was the same, so we just have to multiply both sides by the denominator. If the denominator is not the same then take the lowest common multiple of denominators on both sides, and multiply the equation by it.