Question

Find the value of the variable.

$5x+\left(180-x\right)=300$

Short answer

The value of the variable is $\mathit{x}\mathbf{=}\mathbf{30}$.

Step-by-step solution

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms $5x$and $x$.

$\begin{array}{l}5x+\left(180-x\right)=300\\ 5x+180-x=300\\ 4x+180=300\end{array}$

Step 2. Subtract 180.

To find the value of variable x in the equation $4x+180=300$, subtract 180 from both sides of the equation.

$\begin{array}{l}4x+180-180=300-180\\ 4x=120\end{array}$

Step 3. Divide by 4.

Divide both sides of the equation $4x=120$ by 4 and cancel the common factors of 4 on both sides.

$\begin{array}{l}\frac{4x}{4}=\frac{120}{4}\\ x=\frac{30\times 4}{4}\\ x=30\end{array}$

Step 4. Verify the value.

In order to verify the value of x, substitute 30 for x into the equation $7h+\left(90-h\right)=210$.

$\begin{array}{l}5\times 30+\left(180-30\right)=300\\ 150+150=300\\ 300=300\text{True}\end{array}$

Hence, the value of the variable is $x=30$.