Question

The inequality four fifths minus one half times p is greater than or equal to nine fifths 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)

Answer 1

To solve the inequality 4/5 - 1/2 * p ≥ 9/5 for p, distribute the 1/2, simplify the equation, and isolate p. The solution to the inequality is p ≤ -2. To graph this solution, plot a closed dot at -2 and shade the region to the left of it.

Step-by-step explanation:

To solve the inequality 4/5 - 1/2 * p ≥ 9/5 for p, we can follow these steps:

1. Distribute the 1/2 to both terms in the parentheses: 4/5 - (1/2) * p ≥ 9/5
2. Subtract 4/5 from both sides: - (1/2) * p ≥ 9/5 - 4/5
3. Simplify the right side of the inequality: - (1/2) * p ≥ 5/5
4. Convert the right side to a common denominator: - (1/2) * p ≥ 1
5. Multiply both sides by -2 to isolate p: p ≤ -2

The solution to the inequality is p ≤ -2.

To graph this solution on a number line, we can plot a closed dot at -2 to represent that p is less than or equal to -2. Then, shade the entire region to the left of -2 to indicate all the values that satisfy the inequality.