Q33 - Geometry

Question

Find the value of the variable.

$\left(w-20\right)+5w=28$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{w}\mathbf{=}\mathbf{8}$.

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms w and 5w.

$\begin{array}{l}\left(w-20\right)+5w=28\\ w-20+5w=28\\ 6w-20=28\end{array}$

Step 2. Add 20.

To find the value of variable w in the equation $6w-20=28$, add 20 on both sides of the equation.

$\begin{array}{l}6w-20+20=28+20\\ 6w=48\end{array}$

Step 3. Divide by 6.

Divide both sides of the equation $6w=48$ by 6 and cancel the common factors of 6 on both sides.

$\begin{array}{l}\frac{6w}{6}=\frac{48}{6}\\ w=\frac{6\times 8}{6}\\ w=8\end{array}$

Step 4. Verify the value.

In order to verify the value of w, substitute 8 for w into the equation $\left(w-20\right)+5w=28$.

$\begin{array}{l}\left(8-20\right)+5\times 8=28\\ \left(-12\right)+40=28\\ 28=28\text{ True}\end{array}$

Hence, the value of the variable is $w=8$.