Question 1

Which of the following is the correct interval notation for the solution set of $$x \u003c 5$$?

Accepted Answer

$$(-\infty, 5)$$

Question 2

Solve the inequality $$19 + 7x \geq 2x - 5$$ and write the solution set in interval notation.

Accepted Answer

$$[ -\infty, 4.8 )$$

Question 3

Which of the following inequalities represents the set of all real numbers greater than or equal to $$a$$?

Accepted Answer

$$x \geq a$$

Question 4

Solve the inequality $$7(x - 3) \u003c 2(4x - 1)$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, 5)$$

Question 5

Which of the following is the correct graph for the solution set $$x \geq 2$$?

Accepted Answer

A solid dot at $$x=2$$ with a line extending to the right

Question 6

Solve the inequality $$-3(x-1) \u003c -2[5 + 8(x+5)]$$ and write the solution set in interval notation.

Accepted Answer

$$( -\infty, 4.5 )$$

Question 7

A medical researcher is testing a new drug and needs the dosage $$x (in mg) to be at $$least 12 mg but less than 20 mg. Which interval notation correctly represents the possible dosages?

Accepted Answer

$$[12, 20)$$

Question 8

Solve the inequality $$\frac{1}{2} + \frac{3}{7} \geq \frac{x}{14}$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, 13]$$

Question 9

Solve the inequality $$3(x-6) + 3x - 10 \geq 2(x-8) + 10x$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 10

A chemical reaction requires the temperature $$T to be $$less than or equal to $$100$$ degrees Celsius. Which of the following is the correct interval notation for the acceptable temperature range?

Accepted Answer

$$(-\infty, 100]$$

Question 11

Solve the inequality $$4x + 1 \u003c 4(x - 2)$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, -2)$$

Question 12

Which of the following statements is true about the solution set of $$x \u003e a$$?

Accepted Answer

It includes all real numbers greater than $$a$$

Question 13

A company requires that the number of hours worked per week, $$h$$, must be at least 30 but no more than 40. Which of the following represents this requirement in interval notation?

Accepted Answer

$$[30, 40]$$

Question 14

If $$x \leq 7$$, which of the following is the correct set notation?

Accepted Answer

$$\{ x \mid x \leq 7 \}$$

Question 15

A patient’s blood pressure $$p$$ must be greater than 80 mmHg and less than or equal to 120 mmHg. Which interval notation represents this range?

Accepted Answer

$$(80, 120]$$

Intermediate Algebra: Linear Inequalities and Interval Notation Study Guide

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