Question

1. select all the values of p that are solutions for this inequality.

2.5p - 8 ≥ 12
□ -1 □ 8 □ 0 □ 9 □ 7 □ 12

1. which number line represents the solution set of the inequality

-8t + 2\frac{1}{4} ≥ 42\frac{1}{4}?

1. solve the inequality 1.5g + 12.5 ≤ 35.

g □ < □ ≤ □ = □ ≥ □ >
□ -15 □ -2.5 □ 2.5 □ 15

1. solve the inequality 3.75k + 24.5 < 9.5. complete the sentence to

describe how to graph the solution on a number line.
the solution can be graphed by plotting □ an open circle □ a closed circle at the number
□ -4 □ 4 and shading the number line to the □ left □ right of the circle.

1. solve the inequality 45 ≥ \frac{1}{6}n - 7.

n ≤ □

Explanation:

1. Solving \(2.5p - 8\geq12\)

Step1: Add 8 to both sides

$$2.5p-8 + 8\geq12 + 8$$
$$2.5p\geq20$$

Step2: Divide both sides by 2.5

$$p\geq\frac{20}{2.5}$$
$$p\geq8$$

Step1: Subtract \(2\frac{1}{4}\) from both sides

$$-8t+2\frac{1}{4}-2\frac{1}{4}\geq42\frac{1}{4}-2\frac{1}{4}$$
$$-8t\geq40$$

Step2: Divide both sides by - 8 (and reverse the inequality sign)

$$t\leq\frac{40}{-8}$$
$$t\leq - 5$$

The number line with a closed circle at - 5 (since the inequality is \(\leq\)) and shading to the left. Looking at the options, assume the number - 5 is represented as a closed circle on the number line.

Step1: Subtract 12.5 from both sides

$$1.5g+12.5 - 12.5\leq35 - 12.5$$
$$1.5g\leq22.5$$

Step2: Divide both sides by 1.5

$$g\leq\frac{22.5}{1.5}$$
$$g\leq15$$

Answer:

8, 9, 12

2. Solving \(-8t + 2\frac{1}{4}\geq42\frac{1}{4}\)