Question 1

Which of the following correctly expresses the set of all real numbers $$x$$ such that $$x \geq -3 in $$interval notation?

Accepted Answer

$$[-3, \infty)$$

Question 2

Solve the inequality $$5x - 7 \u003c 18$$ and express the solution in set-builder notation.

Accepted Answer

Question 3

A chemical process is safe only if the temperature $$T (in$$ $$^\circC) $$satisfies $$-20 \leq T \u003c 100. $$Which of the following is the correct interval notation for the safe temperature range?

Accepted Answer

$$[-20, 100)$$

Question 4

Solve the inequality $$-2x + 4 \geq 10$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -3]$$

Question 5

Which of the following is the correct graph representation for the solution set of $$x \u003e 2$$?

Accepted Answer

A number line with an open circle at 2 and shading to the right

Question 6

Solve the three-part inequality $$-4 \u003c 2x + 6 \leq 10$$ and write the solution in interval notation.

Accepted Answer

$$(-5, 2]$$

Question 7

If you multiply both sides of the inequality $$-3x \u003e 9 by$$ $$-1$$, what must you do to the inequality symbol?

Accepted Answer

Reverse the direction of the inequality symbol

Question 8

A medication is effective only if the dosage $$d (in mg) $$satisfies $$d \u003e 50. $$Which of the following is the correct set-builder notation for the effective dosage?

Accepted Answer

$$\{d \mid d \u003e 50\}$$

Question 9

Solve the inequality $$7 - 3x \leq 1$$ and express the solution in set-builder notation.

Accepted Answer

$$\{x \mid x \leq 2\}$$

Question 10

A company requires that the number of hours $$h an $$employee works per week satisfies $$30 \leq h \u003c 40. $$Which of the following is the correct interval notation for the allowed hours?

Accepted Answer

$$[30, 40)$$

Question 11

Which of the following is a solution to the inequality $$2x - 5 \u003e 9$$?

Accepted Answer

$$x = 7$$

Question 12

Solve the inequality $$\frac{1}{2}x - 3 \u003c 5$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 16)$$

Question 13

Which of the following statements is TRUE about the solution set of a linear inequality?

Accepted Answer

It may contain infinitely many solutions

Question 14

A safe blood pressure range for a patient is $$90 \leq p \u003c 120$$ mmHg. Which of the following is the correct set-builder notation for this range?

Accepted Answer

$$\{p \mid 90 \leq p \u003c 120\}$$

Question 15

Solve the three-part inequality $$3 \u003c 2x - 1 \leq 7$$ and express the solution in interval notation.

Accepted Answer

$$(2, 4]$$

Question 16

Which of the following is the correct interval notation for the set $$\{x \mid x \u003c 0\}$$?

Accepted Answer

$$(-\infty, 0)$$

Question 17

If $$x is a $$real number such that $$x \leq 8$$, which of the following is the correct graph representation?

Accepted Answer

A number line with a closed circle at 8 and shading to the left

Question 18

Solve the inequality $$-4x + 9 \u003e 1$$ and express the solution in set-builder notation.

Accepted Answer

$$\{x \mid x \u003c 2\}$$

Question 19

A factory must keep the humidity $$h (in$$ %) between 40% and 60%, including 40% but not 60%. Which of the following is the correct interval notation?

Accepted Answer

$$[40, 60)$$

Question 20

Which of the following is NOT a correct way to represent the solution set of $$x \u003e -2$$?

Accepted Answer

$$[-2, \infty)$$

Linear Inequalities in One Variable: Notation, Solution Methods, and Three-Part Inequalities

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