Question

How do you solve: $\dfrac{1}{2}\left( \left( 360-x \right)-x \right)=75$?

Answer 1

Hint: Simplify the terms inside the bracket and then multiply both the sides of the given equation with 2. Now, rearrange the terms of the given equation by leaving the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S. Now, use simple addition, subtraction to simplify the R.H.S. Make the coefficient of x equal to 1 and accordingly change the R.H.S. to get the answer.

Complete step by step solution:
Here, we have been provided with the equation: $\dfrac{1}{2}\left( \left( 360-x \right)-x \right)=75$ and we are asked to solve this equation. That means we have to find the value of x.
$\because \dfrac{1}{2}\left( \left( 360-x \right)-x \right)=75$
First let us simplify the terms inside the bracket. So, we have,
$\begin{align}
  & \Rightarrow \dfrac{1}{2}\left( \left( 360-x \right)-x \right)=75 \\
 & \Rightarrow \dfrac{1}{2}\left( 360-x-x \right)=75 \\
 & \Rightarrow \dfrac{1}{2}\left( 360-2x \right)=75 \\
\end{align}$
Multiplying both the sides with 2 to remove the fraction in the L.H.S we get,
$\Rightarrow 360-2x=150$
Now, leaving the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow -2x=150-360 \\
 & \Rightarrow -2x=-210 \\
\end{align}\]
Dividing both the sides with -2 we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{-210}{-2} \\
 & \Rightarrow x=105 \\
\end{align}\]

Hence, the value of x is 105.

Note: Remember that to solve an equation means we have to make its coefficient equal to 1. Here, we were provided with only one equation because we were having only one variable x. You can check the answer by substituting the obtained value of x in the equation provided in the question. You have to simplify the L.H.S. by substituting x = 105 and if it equals 75 in the R.H.S then our answer is correct otherwise we need to check the calculation.