Question

In this discussion, you will be demonstrating your understanding of compound inequalities and the effect that dividing by a negative has on an inequality
Your “and” compound inequality is -4 ≤ 3 + 7x < 24
Your “or” compound inequality is    5 – x ≥ 7 or 8x – 3 > 29

- 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

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2. The statement “5–x≥7 or 8x–3>29" is true if at least one of the statements "5–x≥7" and “8x–3>29” are true. The converse is also true. Let A, B, C be the solution sets of “5–x≥7 or 8x–3>29", "5–x≥7" and “8x–3>29”, respectively. Then if x^*∈A, then at least one of the statements x^*∈B and x^*∈C is true. Also, if at least one of the statements x^*∈B and x^*∈C is true, then x^*∈A is also true....

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