Solve the inequality. Graph and check your solution. p - 5 < 1 Choose the correct answer below.
A. p < 6
B. p > 6
C. p < - 4
D. p > - 4
To solve the inequality p - 5 < 1, we can add 5 to both sides to isolate p:
p - 5 + 5 < 1 + 5
p < 6
So the correct answer is A. p < 6.
To solve the inequality p - 5 < 1, we need to isolate the variable p.
Adding 5 to both sides of the inequality, we get:
p - 5 + 5 < 1 + 5
p < 6
So the solution to the inequality is p < 6.
To graph the solution, we can draw a number line and mark the number 6 with an open circle, indicating that 6 is not included in the solution. Then, we shade the region to the left of 6, since all values less than 6 satisfy the inequality.
To check our solution, we can pick a value to the left of 6 (for example, p = 0) and substitute it into the original inequality:
0 - 5 < 1
-5 < 1 (which is true)
Therefore, the correct answer is A. p < 6.
To solve the inequality p - 5 < 1, we can isolate the variable p by adding 5 to both sides of the inequality:
p - 5 + 5 < 1 + 5
This simplifies to:
p < 6
So the correct answer is A. p < 6.
To graph the solution, we plot a number line and mark the value 6 with an open circle. Since p is less than 6, we shade the region to the left of the open circle to indicate all values of p that satisfy the inequality.
To check the solution, we can choose any value less than 6, substitute it into the original inequality, and see if it holds. For example, let's choose p = 5:
5 - 5 < 1
This simplifies to:
0 < 1
Since 0 is indeed less than 1, the inequality holds true.