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
Choose the graph below
To solve the inequality, we need to isolate the variable p. Starting with p - 5 < 1, we can add 5 to both sides to get p < 6. Therefore, the correct answer is A. p < 6.
The graph of the solution is a number line with an open circle at 6, indicating that 6 is not included in the solution, and an arrow pointing to the left, indicating that all values less than 6 satisfy the inequality.
To solve the inequality p - 5 < 1, we can add 5 to both sides of the inequality:
p - 5 + 5 < 1 + 5
This simplifies to:
p < 6
Therefore, the correct answer is A. p < 6.
To graph this solution, we can draw a number line and mark the point 6 with an open circle (since the inequality is "less than"):
-------------o-----------------------
-4 -3 -2 -1 0 1 2 3 4 5 6 7
Next, we can shade the region to the left of 6, since the solution is p < 6:
<--------------o--------------------
-4 -3 -2 -1 0 1 2 3 4 5 6 7
To check our solution, we can choose a value for p in the shaded region, such as p = 5. Plugging this value into the original inequality, we get:
p - 5 < 1
5 - 5 < 1
0 < 1
Since 0 is indeed less than 1, our solution is confirmed.
To solve the inequality p - 5 < 1, we need to isolate the variable p.
First, let's add 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 can represent all the values of p that satisfy the inequality on a number line. We know that p is less than 6, so we draw an open circle at 6 and shade to the left.
The graph should look like this:
-10 -5 0 5 10
----|----|----|----|----|----|
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To check the solution, we can substitute a value within the shaded region into the original inequality and see if it holds true. For example, if we substitute p = 4 into the inequality, we get:
4 - 5 < 1
-1 < 1
Since -1 is indeed less than 1, the solution p < 6 is correct.