Solve |P| > 3
{P|-3 < P < 3}
{-3, 3}
{P|P < -3 or P > 3}\
The solution to |P| > 3 is {P|P < -3 or P > 3}. This means that the set of values for P that satisfy the inequality is all real numbers less than -3 or all real numbers greater than 3.
To solve the inequality |P| > 3, we need to consider two cases:
Case 1: P is positive or zero:
In this case, the absolute value of P is equal to P. So, the inequality can be written as P > 3.
Case 2: P is negative:
In this case, the absolute value of P is equal to -P. So, the inequality can be written as -P > 3. To solve this inequality, we need to multiply both sides by -1, but remember to reverse the inequality symbol. Therefore, we have P < -3.
Combining the solutions from both cases, we have two separate inequalities:
1. P > 3
2. P < -3
Now, let's consider the given sets:
1. {P|-3 < P < 3}
This set includes all values of P that are greater than -3 and less than 3. However, we need to solve the inequality |P| > 3, which means P can also be greater than 3 or less than -3.
2. {-3, 3}
This set includes the specific values -3 and 3, but it does not represent the complete solution to the inequality |P| > 3.
3. {P|P < -3 or P > 3}
This set includes all values of P that are less than -3 or greater than 3. It represents the complete solution to the inequality |P| > 3.
Therefore, the correct solution to the inequality |P| > 3 is given by the set {P|P < -3 or P > 3}.
To solve the inequality |P| > 3, we need to consider two cases: when P is positive and when P is negative.
Case 1: P is positive
When P is positive, the absolute value of P is equal to P. So, the inequality becomes P > 3.
Therefore, the solution for positive P is P > 3.
Case 2: P is negative
When P is negative, the absolute value of P is equal to -P. So, the inequality becomes -P > 3.
To solve for P in this case, we need to flip the inequality sign when multiplying or dividing by a negative number. Dividing both sides of the equation by -1, we have P < -3.
Therefore, the solution for negative P is P < -3.
Combining both cases, the solution to the inequality |P| > 3 is P > 3 or P < -3.
Now, let's consider the given sets:
Set 1: {P | -3 < P < 3}
The set contains numbers greater than -3 and less than 3. However, this set does not include the values that satisfy the inequality |P| > 3. Therefore, this set is not the solution.
Set 2: {-3, 3}
This set includes the numbers -3 and 3, which satisfy the inequality |P| > 3. Therefore, this set is part of the solution.
Set 3: {P | P < -3 or P > 3}
This set includes all the values smaller than -3 and all the values greater than 3, which satisfy the inequality |P| > 3. Therefore, this set is another representation of the solution.
In conclusion, the solution to the inequality |P| > 3 is P > 3 or P < -3, which is represented by Set 2 {-3, 3} or Set 3 {P | P < -3 or P > 3}.