Using the variable x to represent the number, we have:
Five times a number: 5x
Six more than five times a number: 5x + 6
the number increased by eighteen: x + 18
So, equating the expressions 5x + 6 and x + 18, we have our equation:
![5x+6=x+18](https://img.qammunity.org/2023/formulas/mathematics/college/f3kfys4bnephr5ezb4103lyt8f1movptbn.png)
Now, solving the equation for x, we have:
![\begin{gathered} 5x-x=18-6 \\ 4x=12 \\ x=(12)/(4) \\ x=3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1wc7nmkaspmfdv7ha7hcqz4fxxptxnzy2f.png)
So the number we want is x = 3.