Q: Which of the following is the correct graph for the solution set of $x + 8 < 0$?

A number line with an open circle at $-8$ and shading to the left.

Question 1

Which of the following represents the solution set in interval notation for the compound inequality $x + 8 < 0$ or $7x > -35$?

Accepted Answer

$(-\infty, -8) \cup (-5, \infty)$

Question 2

What is the solution to the inequality $x + 8 < 0$?

Accepted Answer

$x < -8$

Question 3

Solve the inequality $7x > -35$ and express the solution in interval notation.

Accepted Answer

$(-5, \infty)$

Question 4

Which of the following best describes the solution set of a compound inequality formed by the word 'or'?

Accepted Answer

The union of the solution sets of the two inequalities.

Question 5

If $x + 8 < 0$ or $7x > -35$, which of the following values of $x$ is NOT in the solution set?

Accepted Answer

$x = -7$

Question 6

Which of the following statements is true about the solution set of $x + 8 < 0$ or $7x > -35$?

Accepted Answer

It includes all $x$ such that $x < -8$ or $x > -5$.

Question 7

A chemical process is safe if the temperature $T$ satisfies $T + 8 < 0$ or $7T > -35$. Which temperature is NOT safe?

Accepted Answer

$T = -7$

Question 8

Which step is necessary to isolate $x$ in the inequality $x + 8 < 0$?

Accepted Answer

Subtract 8 from both sides.

Question 9

If a patient’s blood pressure $x$ must satisfy $x + 8 < 0$ or $7x > -35$ to be considered at risk, which of the following values is considered at risk?

Accepted Answer

$x = -10$

Question 10

Which of the following is the correct graph for the solution set of $x + 8 < 0$?

Accepted Answer

A number line with an open circle at $-8$ and shading to the left.

Question 11

Which interval notation represents all real numbers less than $-8$?

Accepted Answer

$(-\infty, -8)$

Question 12

A company will hire applicants if their test score $x$ satisfies $x + 8 < 0$ or $7x > -35$. Which score will NOT result in being hired?

Accepted Answer

$x = -7$

Question 13

Which of the following is the correct solution to $7x > -35$?

Accepted Answer

$x > -5$

Question 14

If $x$ represents the number of hours a student studies and must satisfy $x + 8 < 0$ or $7x > -35$ to qualify for a special program, which of the following is NOT a qualifying value?

Accepted Answer

$x = -7$

Question 15

Which of the following best describes the union of the solution sets for $x < -8$ and $x > -5$?

Accepted Answer

$(-\infty, -8) \cup (-5, \infty)$

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

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