Q31 - Geometry

Question

Find the value of the variable.

$\left(2g-15\right)+g=9$

Step-by-Step Solution

Answer

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

Step 1. Combine the like terms.

First, remove all the brackets and combine the like terms 2g and g.

$\begin{array}{l}\left(2g-15\right)+g=9\\ 2g-15+g=9\\ 3g-15=9\end{array}$

Step 2. Add 15.

To find the value of variable g in the equation $3g-15=9$, add 15 on both sides of the equation.

$\begin{array}{l}3g-15+15=9+15\\ 3g=24\end{array}$

Step 3. Divide by 3.

Divide both sides of the equation $3g=24$ by 3 and cancel the common factors of 3 on both sides.

$\begin{array}{l}\frac{3g}{3}=\frac{24}{3}\\ g=\frac{3\times 8}{3}\\ g=8\end{array}$

Step 4. Verify the value.

In order to verify the value of g, substitute 8 for g into the equation $\left(2g-15\right)+g=9$.

$\begin{array}{l}\left(2\times 8-15\right)+8=9\\ \left(16-15\right)+8=9\\ 1+8=9\\ 9=9\text{ True}\end{array}$

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