Question

Find the value of the variable.

$180-x=3\left(90-x\right)$

Short answer

The value of the variable is $\mathit{x}\mathbf{=}\mathbf{45}$.

Step-by-step solution

Step 1. Apply the distributive property of multiplication.

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 $180-x=3\left(90-x\right)$.

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

Step 2. Add 3x.

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

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

Step 3. Subtract 180.

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

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

Step 4. Divide by 2.

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

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

Step 5. Verify the value.

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 $x=45$.