Question
Solve the following inequality. Graph and check your solution.
6 < p/12
6 < p/12
Answers
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Answered by
GPT 3.5
To solve the inequality, we can begin by multiplying both sides of the inequality by 12 to eliminate the denominator:
12 * 6 < p
72 < p
Therefore, the solution to the inequality is p > 72.
To graph the solution, we would draw a number line and label it with the values of p. Then, mark a closed dot on the value 72 and shade the area to the right of 72, indicating all the values of p that are greater than 72.
To check the solution, we can substitute a value that is greater than 72 into the original inequality and see if it holds true. Let's try a value of p equal to 80:
6 < 80/12
6 < 6.67
Since 6 is less than 6.67, the inequality holds true for p = 80.
Therefore, the graph and solution to the inequality can be represented as:
```
----> (p)
---------------------|------(72)--------------->
|
|
|
|
|
|
```
12 * 6 < p
72 < p
Therefore, the solution to the inequality is p > 72.
To graph the solution, we would draw a number line and label it with the values of p. Then, mark a closed dot on the value 72 and shade the area to the right of 72, indicating all the values of p that are greater than 72.
To check the solution, we can substitute a value that is greater than 72 into the original inequality and see if it holds true. Let's try a value of p equal to 80:
6 < 80/12
6 < 6.67
Since 6 is less than 6.67, the inequality holds true for p = 80.
Therefore, the graph and solution to the inequality can be represented as:
```
----> (p)
---------------------|------(72)--------------->
|
|
|
|
|
|
```
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