Question

1. which graph represents the solution to -2x - 3 > -7? a. graph with arrow ending at 2 with an open - circle b. graph with arrow starting at 2 with an open - circle c. graph with arrow ending at 5 with an open - circle d. graph with arrow starting at 5 with an open - circle 2. which expression represents a natural number? a. |-6|-|-8| b. -|11 - 15| c. -|-7|-|16| d. -|1|+|-3| 3. simplify the expression below. $\frac{5}{6}(12p - 42)$ 4. ross joined a 30 - week weight loss challenge. he lost 10.4 pounds in the first 4 weeks. if he maintains this rate of weight loss, how many pounds would he lose at the end of the 30 - week challenge? a. 74 pounds b. 76 pounds c. 78 pounds d. 82 pounds

Explanation:

Step1: Solve the inequality -2x - 3 > -7

Add 3 to both sides: -2x - 3+3 > -7 + 3, which simplifies to -2x > -4. Then divide both sides by -2 and reverse the inequality sign (since dividing by a negative number), getting x < 2. The graph with an open - circle at 2 and an arrow pointing to the left represents this solution. So the answer to question 1 is A.

Step2: Evaluate each option for question 2

A. \(|-6|-|-8|=6 - 8=-2\); B. \(-|11 - 15|=-|-4|=-4\); C. \(-|-7|-|16|=-7 - 16=-23\); D. \(-|1|+|-3|=-1 + 3 = 2\), which is a natural number. So the answer to question 2 is D.

Step3: Simplify the expression \(\frac{5}{6}(12p - 42)\)

Use the distributive property: \(\frac{5}{6}\times12p-\frac{5}{6}\times42 = 10p-35\). So the answer to question 3 is \(10p - 35\).

Step4: Find the rate of weight - loss and total weight - loss for question 4

The rate of weight - loss in the first 4 weeks is \(\frac{10.4}{4}=2.6\) pounds per week. For a 30 - week challenge, the total weight - loss is \(2.6\times30 = 78\) pounds. So the answer to question 4 is C.

Answer:

1. A.
2. D.
3. \(10p - 35\)
4. C.