Q42 - Geometry

Question

Find the value of the variable.

$\left(3g-4\right)+\left(4g+10\right)=90$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{g}\mathbf{=}\mathbf{12}$.

Step 1. Combine the like terms.

First remove all the brackets and combine the like terms.

$\begin{array}{r}\left(3g-4\right)+\left(4g+10\right)=90\\ 3g-4+4g+10=90\\ 7g+6=90\end{array}$

Step 2. Subtract 6.

To find the value of variable g in the equation $7g+6=90$, subtract 6 from both sides of the equation.

$\begin{array}{l}7g+6-6=90-6\\ 7g=84\end{array}$

Step 3. Divide by 7.

Divide both sides of the equation $7g=84$ by 7 and cancel the common factors of 7 on both sides.

$\begin{array}{l}\frac{7g}{7}=\frac{84}{7}\\ g=\frac{12\times 7}{9}\\ g=12\end{array}$

Step 4. Verify the value.

In order to verify the value of g, substitute 12 for g into the equation $\left(3g-4\right)+\left(4g+10\right)=90$.

$\begin{array}{l}\left(3\times 12-4\right)+\left(4\times 12+10\right)=90\\ \left(36-4\right)+\left(48+10\right)=90\\ 32+58=90\\ 90=90\text{ True}\end{array}$

Hence, the value of the variable is $g=12$.