• Given the description "Six increased by twice a number is no more than 20", you need to know the following:
- In this case, the word "increased" indicates an Addition.
- The word "twice" indicates a Multiplication by 2.
- "No more than" indicates that six increased by twice a number must be less than or equal to 20.
- The inequality symbol whose meaning is "Less than or equal to" is:
[tex]\leq[/tex]Knowing the information shown before, you can write the following expression to represent "Six increased by twice a number" (Let be "x" the unknown number):
[tex]6+2x[/tex]Therefore, you can write the following inequality that models the description given in the exercise:
[tex]6+2x\leq20[/tex]• Now you need to solve it:
1. Apply the Subtraction Property of Inequality by subtracting 6 from both sides of the inequality:
[tex]\begin{gathered} 6+2x-(6)\leq20-(6) \\ \\ 2x\leq14 \end{gathered}[/tex]2. Apply the Division Property of Inequality by dividing both sides of the inequality by 2:
[tex]\begin{gathered} \frac{2x}{2}\leq\frac{14}{2} \\ \\ x\leq7 \end{gathered}[/tex]• In order to graph the solution on a Number Line, you can follow these steps:
- Since the inequality symbol indicates that "x" is less than 7, it indicates that 7 is included in the solution. Therefore, you must draw a closed circle over that value.
- Draw a line from the circle to the left.
Then, you get:
Hence, the answer is:
- Inequality:
[tex]6+2x\leq20[/tex]- Solution:
[tex]x\leq7[/tex]- Number Line:
