Question

PLEASE HELP!!! I NEED THIS SLOVED AND EXPLAINED QUICKLY.

(Two-Step Linear Inequalities HC)

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

Shade the region to the left of -2 (including -2) on a number line is p ≤ -2.

Part A:

To solve the inequality $\dfrac{4}{5}-\dfrac12p \ge \dfrac95$, we manipulate it step-by-step as follows:

`(4)/(5)-\frac12p &\ge \frac95 \`

`(5)/(5) \cdot \left((4)/(5)-\frac12p \right) &\ge (5)/(5) \cdot \left(\frac95 \right) \quad (\text{multiply both sides by }(5)/(5))\`

`(4)/(5)-\frac52p &\ge \frac95 \`

10
`\cdot \left((4)/(5)-\frac52p \right) &\ge 10 \cdot \left(\frac95 \right) \quad (\text{multiply both sides by }10)\`

`8-5p &\ge 18 \8-5p-8 &\ge 18-8 \quad (\text{subtract }8 \text{ from both sides})\-5p &\ge 10 \`

`\frac{-5p}{{-5}} &\le \frac{10}{{-5}} \quad (\text{divide both sides by }-5, \text{flip the inequality})\`

`p &\le -2`

Therefore, the solution to the inequality is
`$p\le -2$`.

Part B:

To graph the solution
`$p\le -2$` on a number line, first draw a number line and mark a point at -2. Shade the region to the left of -2 (including -2 itself) since all values of p that are less than or equal to -2 satisfy the inequality.

Here's how the graph would look like:

|-------|-------|-------|-------|-------|-------|

-5 -4 -3 -2 -1 0