Question 1

Solve the compound inequality $$\frac{1}{7}x + 2 \geq 3$$ and $$\frac{1}{5}x - 3 \geq 1. $$What is the solution set in interval notation?

Accepted Answer

$$[15, \infty)$$

Question 2

Solve the compound inequality $$\frac{1}{3} \leq \frac{4}{3}x + 2 \leq 4. $$What is the solution set in interval notation?

Accepted Answer

$$\left[ -\frac{5}{4}, \frac{3}{2} \right]$$

Question 3

A chemical process requires the temperature $$T (in$$ $$^\circC) to $$satisfy $$20 \leq T \u003c 80. $$Which of the following is the correct interval notation for the acceptable temperature range?

Accepted Answer

$$[20, 80)$$

Question 4

A medication is effective only if the patient's blood pressure $$P (in $$mmHg) satisfies $$90 \u003c P \leq 120. $$Which of the following is the correct interval notation for $$P$$?

Accepted Answer

$$(90, 120]$$

Question 5

Solve the compound inequality $$2x - 5  0. $$What is the solution set in interval notation?

Accepted Answer

$$(-3, 6)$$

Question 6

A company requires that the number of hours $$h an $$employee works per week satisfies $$30 \leq h \leq 40. $$Which of the following is the correct interval notation?

Accepted Answer

$$[30, 40]$$

Question 7

Solve the compound inequality $$-2 \leq 3x + 1 \u003c 7. $$What is the solution set in interval notation?

Accepted Answer

$$\left[ -1, 2 \right)$$

Question 8

A safe dosage of a drug requires the concentration $$c (in mg/L) to $$satisfy $$0.5 \leq c \u003c 2.0. $$Which of the following is the correct interval notation?

Accepted Answer

$$[0.5, 2.0)$$

Question 9

Solve the compound inequality $$4 \u003c 2x + 6 \leq 10. $$What is the solution set in interval notation?

Accepted Answer

$$( -1, 2 ]$$

Question 10

A historical event occurred between the years 1920 and 1945, inclusive of 1920 but not 1945. Which interval notation correctly represents the possible years?

Accepted Answer

$$[1920, 1945)$$

Question 11

Solve the compound inequality $$-5 \u003c x - 2 \leq 3. $$What is the solution set in interval notation?

Accepted Answer

$$(-3, 5]$$

Question 12

A solution is only stable if its pH $$p$$ satisfies $$6.5 \leq p \leq 7.5. $$Which of the following is the correct interval notation?

Accepted Answer

$$[6.5, 7.5]$$

Question 13

Solve the compound inequality $$3 \leq 2x - 1 \u003c 9. $$What is the solution set in interval notation?

Accepted Answer

$$[2, 5)$$

Question 14

A car rental company allows customers to rent a car for $$d$$ days, where $$1 \u003c d \leq 14. $$Which of the following is the correct interval notation?

Accepted Answer

$$(1, 14]$$

Question 15

Solve the compound inequality $$-4 \leq 5x + 6 \u003c 11. $$What is the solution set in interval notation?

Accepted Answer

$$\left[ -2, 1 \right)$$

Question 16

A laboratory experiment requires the pressure $$P (in $$atm) to be at least 1.2 but less than 2.5. Which interval notation represents this requirement?

Accepted Answer

$$[1.2, 2.5)$$

Step-by-Step Guidance for Compound Inequalities (Section 2.5)

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