Solve the following inequality. Graph and check your solution.
6 < p/12
To solve the inequality 6 < p/12, we can multiply both sides of the inequality by 12 to eliminate the fraction:
6 * 12 < p
72 < p
So, the solution to the inequality is p > 72.
To graph the solution, we can represent the numbers greater than 72 on a number line. We will use an open circle at 72 to indicate that 72 itself is not included in the solution.
--------------------O----------------------->
Now, we can check the solution by picking a value greater than 72 and plugging it into the original inequality. Let's choose p = 80:
6 < 80/12
6 < 6.67
Since 6 is indeed less than 6.67, the inequality holds true. Thus, the solution p > 72 is correct.
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)--------------->
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```
To solve the inequality 6 < p/12, we will isolate p on one side of the inequality symbol.
First, we will multiply both sides of the inequality by 12 to cancel out the denominator:
6 * 12 < p/12 * 12
72 < p
Now we have the inequality 72 < p. This means that p is greater than 72.
To graph the solution, we will plot the numbers on a number line. Since p is greater than 72, we will use an open circle on 72 and shade the region to the right of 72.
To check the solution, substitute a value greater than 72 into the original inequality and see if it is true. For example, let's substitute 80:
6 < 80/12
6 < 6.67
Since 6 is less than 6.67, the inequality is true. Therefore, the solution is correct.
The solution to the inequality 6 < p/12 is p > 72, and the graph shows an open circle on 72 with shading to the right.