Q: Which of the following is the correct process to solve $6(x-5)<12$?

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

Q: Which of the following best describes the graph of the solution set to $6(x-5)<12$?

A ray extending left from 7, not including 7

Question 1

Which of the following best describes the solution set to the compound inequality $6(x-5)<12 \ 	ext{or}\ x+7>10$?

Accepted Answer

$(-\infty, \infty)$

Question 2

What is the solution to the inequality $6(x-5)<12$?

Accepted Answer

$x<7$

Question 3

Solve the inequality $x+7>10$ 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 $6(x-5)<12 \ 	ext{or}\ x+7>10$?

Accepted Answer

$x=8$

Question 6

A student claims that the solution to $6(x-5)<12 \ 	ext{or}\ x+7>10$ 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 $x<7$?

Accepted Answer

$(-\infty, 7)$

Question 8

If $x=5$, which inequalities from $6(x-5)<12$ or $x+7>10$ does it satisfy?

Accepted Answer

It satisfies only $6(x-5)<12$.

Question 9

Which of the following is the correct process to solve $6(x-5)<12$?

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 $6(T-5)<12$ or $T+7>10$. For which temperature ranges is the process safe?

Accepted Answer

$T<7$ or $T>3$, which is $(-\infty, \infty)$

Question 11

Which of the following best describes the graph of the solution set to $6(x-5)<12$?

Accepted Answer

A ray extending left from 7, not including 7

Question 12

If a patient’s blood pressure $x$ must satisfy $x+7>10$ for a medication to be administered, what is the minimum blood pressure required?

Accepted Answer

$x>3$

Question 13

Which of the following is true about the solution set to $6(x-5)<12 \ 	ext{or}\ x+7>10$?

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 $6(x-5)<12$ and $x+7>10$?

Accepted Answer

It satisfies only $x+7>10$.

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

Study Guide - Practice Questions

Study Guide - Flashcards