91Ó°ÊÓ

The formula of distributive property of multiplication is given by: $x\left(y+z\right)=xy+xz$. Apply this property to the right-hand side of the equation $180−x=3\left(90−x\right)$.

$\begin{array}{l}180−x=3\left(90−x\right)\\ 180−x=3×90−3×x\\ 180−x=270−3x\end{array}$

To further simplify, add 3x from both sides of the equation $180−x=270−3x$.

$\begin{array}{l}180−x+3x=270−3x+3x\\ 180+2x=270\end{array}$

To find the value of the variable x in the equation $180+2x=270$, subtract 180 from both sides of the equation.

$\begin{array}{l}180+2x−180=270−180\\ 2x=90\end{array}$

Divide both sides of the equation $2x=90$by 2 and cancel the common factors of 2 on both sides.

$\begin{array}{l}\frac{2x}{2}=\frac{90}{2}\\ x=\frac{45×2}{2}\\ x=45\end{array}$

In order to verify the value of x, substitute 45 for x into the equation $180−x=3\left(90−x\right)$.

$\begin{array}{l}180−45=3\left(90−45\right)\\ 135=3\left(45\right)\\ 135=135\text{True}\end{array}$

Hence, the value of the variable is $x=45$.