Question 1

Which of the following represents the interval notation for the inequality $$1 \leq x \leq 3$$?

Accepted Answer

$$[1, 3]$$

Question 2

Given the inequality $$-4 \u003c x \u003c 0$$, which graph best represents the solution?

Accepted Answer

A number line with open circles at $$-4$$ and $$0$$, and a shaded region between them.

Question 3

Which property of inequalities explains why multiplying both sides of $$a \u003c b by a $$negative number reverses the inequality?

Accepted Answer

Multiplication property for $$c \u003c 0$$

Question 4

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

Accepted Answer

$$(-1, \infty)$$

Question 5

Which of the following is the correct interval notation for $$x \u003e 5$$?

Accepted Answer

$$(5, \infty)$$

Question 6

If $$a \u003c b$$, which of the following is always true for any real number $$c$$?

Accepted Answer

$$a + c \u003c b + c$$

Question 7

Solve the compound inequality $$-5 \u003c 3x - 2 \u003c 1$$ for $$x.$$

Accepted Answer

Question 8

Which of the following is the correct solution to $$4x + 7 \geq 2x - 3$$?

Accepted Answer

$$x \geq -5$$

Question 9

When solving $$-1 \leq \dfrac{3 - 5x}{2} \leq 9$$, what is the solution for $$x in $$interval notation?

Accepted Answer

$$[-1.6, 3.2]$$

Question 10

Which of the following is NOT a linear inequality?

Accepted Answer

$$x^2 - 4$$ \u003c 0$$

Question 11

A chemical process requires the temperature $$T to be $$between $$-10^{\circ}C $$and $$50^{\circ}C$$, inclusive. Which interval notation correctly represents the acceptable temperature range?

Accepted Answer

$$[-10, 50]$$

Question 12

If $$a \u003c b$$ and $$c \u003c 0$$, which of the following is true after multiplying both sides by $$c$$?

Accepted Answer

$$ac \u003e bc$$

Question 13

Which interval notation represents all real numbers?

Accepted Answer

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

Question 14

A medical test result is considered normal if $$x \leq 1. $$Which interval notation represents the set of normal results?

Accepted Answer

$$(-\infty, 1]$$

Question 15

Which of the following is the correct interval notation for the solution to $$x \u003c 0$$?

Accepted Answer

$$(-\infty, 0)$$

Question 16

A factory can operate only if the pressure $$p$$ satisfies $$p \geq 2. $$Which interval notation represents the set of allowable pressures?

Accepted Answer

$$[2, \infty)$$

Question 17

Which of the following is the correct solution to the inequality $$5 \u003c 3n - 2 \u003c 1$$?

Accepted Answer

No solution

Question 18

If $$a  0$$, what is the result of multiplying both sides by $$c$$?

Accepted Answer

$$ac \u003c bc$$

Question 19

Which interval notation represents the solution to $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 20

A historical event occurred between the years 1900 and 1950, not including 1950. Which interval notation best represents the years during which the event could have occurred?

Accepted Answer

$$[1900, 1950)$$

Linear Inequalities and Interval Notation in Precalculus

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