Question

Which of the following is the solution to the compound inequality below?

5 + x2 3 or 6x + 1 < -29
A. x2 - 10 or x < -14/3
B. x2 - 2 or x < -5
C. x2 or x < -5
D. x2 + 8 or x < -14/3

Answer 1

To solve the compound inequality 5 + x² / 3 or 6x + 1 < -29, we need to solve each inequality separately and find the values of x for which both inequalities are true. The solution to the compound inequality is x < -5. The correct option is C. x² or x < -5.

Step-by-step explanation:

To solve the compound inequality 5 + x² / 3 or 6x + 1 < -29, we need to solve each inequality separately and find the values of x for which both inequalities are true. Let's start with the first inequality:

5 + x² / 3 < -29

Subtracting 5 from both sides gives:

x² / 3 < -34

Multiplying both sides by 3 gives:

x² < -102

Since a square is always positive or zero, there is no real solution to this inequality. Now, let's solve the second inequality:

6x + 1 < -29

Subtracting 1 from both sides gives:

6x < -30

Dividing both sides by 6 gives:

x < -5

Therefore, the solution to the compound inequality is x < -5. The correct option is C. x² or x < -5.