Question 1

Which of the following best describes the solution set to the compound inequality $$6(x-5)10$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 2

What is the solution to the inequality $$6(x-5)\u003c12$$?

Accepted Answer

$$x\u003c7$$

Question 3

Solve the inequality $$x+7\u003e10$$ and express the solution in interval notation.

Accepted Answer

$$(3, \infty)$$

Question 4

If a compound inequality is formed by the word "or," what does its solution set represent?

Accepted Answer

The union of the solution sets of the two inequalities

Question 5

Which of the following values is a solution to $$6(x-5)10$$?

Accepted Answer

$$x=8$$

Question 6

A student claims that the solution to $$6(x-5)10 is$$ $$(3,7). $$What is the error in this reasoning?

Accepted Answer

The student found the intersection instead of the union of the solution sets.

Question 7

Which interval notation represents the solution set to $$x\u003c7$$?

Accepted Answer

$$(-\infty, 7)$$

Question 8

If $$x=5$$, which inequalities from $$6(x-5)10$$ does it satisfy?

Accepted Answer

It satisfies only $$6(x-5)\u003c12.$$

Question 9

Which of the following is the correct process to solve $$6(x-5)\u003c12$$?

Accepted Answer

Divide both sides by 6, then add 5 to both sides.

Question 10

A real-world scenario: A chemical process is safe if the temperature $$T (in$$ $$^	ext{o}C) $$satisfies $$6(T-5)10. $$For which temperature ranges is the process safe?

Accepted Answer

$$T3$$, which is $$(-\infty, \infty)$$

Question 11

Which of the following best describes the graph of the solution set to $$6(x-5)\u003c12$$?

Accepted Answer

A ray extending left from 7, not including 7

Question 12

If a patient’s blood pressure $$x$$ must satisfy $$x+7\u003e10$$ for a medication to be administered, what is the minimum blood pressure required?

Accepted Answer

$$x\u003e3$$

Question 13

Which of the following is true about the solution set to $$6(x-5)10$$?

Accepted Answer

It includes all real numbers.

Question 14

What is the union of the solution sets $$(-\infty, 7)$$ and $$(3, \infty)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 15

If $$x=7$$, which of the following is true for the inequalities $$6(x-5)10$$?

Accepted Answer

It satisfies only $$x+7\u003e10.$$

Solving Compound Inequalities with 'Or' (Union of Solution Sets)

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