### Description

For this problem you will be demonstrating your understanding of compound inequalities and the effect that dividing by a negative has on an inequality. Read the following instructions in order and view the example to complete this discussion: According to the first letter of your last name, find the pair of compound inequalities assigned to you in the table below.

Your “and” compound inequality is -17 < 3 + 10x ≤ 33 And Your “or” compound inequality is 5x + 3 ≤ -2 or 13 – x ≤ 6 Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, being careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions.

Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated in the Instructor Guidance in the left navigation toolbar.

Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.): Compound inequalities And Or Intersection Union

## Explanation & Answer

5x+3 <= -2

5x <= -2-3

5x <= -5

x <= -5/5

x<= -1

13-x < =6

13-6 <= x

7 <= x

x>=7

**x< = -1 or x>= 7**