The inequality three fourths minus one half times p is greater than five fourths is given.
Part A: Solve the inequality for p. Show each step of your work. (2 points)
Part B: How would you graph your solution to Part A on a number line? Explain in words. (2 points)
Part A:
We are given the inequality: 3/4 - 1/2*p > 5/4
First, let's simplify the expression on the left side of the inequality:
3/4 - 1/2*p = 2/4 - 1/2*p
= 2/4 - 2/4*p
= 2/4(1 - p)
Now, we have: 2/4(1 - p) > 5/4
Next, let's multiply both sides of the inequality by 4/2 to get rid of the fraction on the left side:
2/4(1 - p) * 4/2 > 5/4 * 4/2
1 - p > 10/4
1 - p > 2 + 1/2
Now, let's subtract 1 from both sides of the equation:
1 - p - 1 > 2 + 1/2 - 1
-p > 1/2
Next, let's multiply both sides of the inequality by -1 (remember that when we multiply or divide by a negative number, the direction of the inequality sign flips):
-p * -1 < 1/2 * -1
p < -1/2
Therefore, the solution to the inequality is p < -1/2.
Part B:
To graph the solution p < -1/2 on a number line, we can start by plotting a point at -1/2 and then shading all the values to the left of that point. This represents all the values of p that are less than -1/2. Since the inequality is strict (p < -1/2), we would use an open circle at -1/2 to indicate that the value -1/2 is not included in the solution set.