Question 1

Which of the following best describes the difference between an equation and an inequality?

Accepted Answer

An equation uses the symbol $$=$$, while an inequality uses symbols such as $$, $$\leq$$, or $$\geq$$.

Question 2

Solve the inequality $$3x - 2 \u003e 1$$ and express the solution in interval notation.

Accepted Answer

$$(1, \infty)$$

Question 3

A laboratory needs to keep the temperature of a chemical reaction below $$50^\circC $$for safety. If the temperature $$T in $$degrees Celsius is modeled by $$T = 2x + 10$$, where $$x is $$the number of minutes since the reaction started, for which values of $$x is $$the reaction safe?

Accepted Answer

$$x \u003c 20$$

Question 4

Which of the following is the correct interval notation for the solution to $$x \leq 4$$?

Accepted Answer

$$(-\infty, 4]$$

Question 5

Solve the compound inequality $$2x + 3 \u003c -1$$ and express the solution in interval notation.

Accepted Answer

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

Question 6

A company requires that the number of hours $$h an $$employee works per week must be at least 30 but less than 40. Which of the following represents this requirement in interval notation?

Accepted Answer

$$[30, 40)$$

Question 7

Solve for $$x$$: $$3(x - 2) \u003e 4x + 7$$

Accepted Answer

$$x \u003c -13$$

Question 8

Which of the following statements about inequalities is TRUE?

Accepted Answer

Multiplying both sides of an inequality by a negative number reverses the direction of the inequality sign.

Question 9

A medication is effective only if the concentration $$C in $$the bloodstream satisfies $$5 \leq C \u003c 12 mg/L. $$Which of the following is the correct interval notation for the effective concentration?

Accepted Answer

$$[5, 12)$$

Question 10

Solve the inequality $$4x + 3(x + 1) \u003c -2(x - 3)$$ for $$x.$$

Accepted Answer

$$x \u003c -13$$

Question 11

If $$x is a $$solution to the inequality $$x \u003e -2$$ and $$x \u003c 5$$, which of the following is the correct interval notation for all possible values of $$x$$?

Accepted Answer

$$(-2, 5)$$

Question 12

A car rental company charges a base fee of $$\20$ plus $$\$$0.50$$ per mile driven. If a customer wants to spend no more than $$\50$, what is the maximum number of miles m$ they can drive? (Express your answer as an inequality.)

Accepted Answer

$$0.5m + 20 \leq 50$$

Question 13

Which of the following is the solution set for the inequality $$-3x \u003e 9$$?

Accepted Answer

$$x \u003c -3$$

Question 14

A student must score at least 70 but less than 90 to pass a course with distinction. If $$s is $$the student's score, which of the following inequalities represents this requirement?

Accepted Answer

$$70 \leq s \u003c 90$$

Question 15

Solve the inequality $$2 - 5x \leq 12$$ for $$x.$$

Accepted Answer

$$x \leq -2$$

Question 16

Which of the following is the correct graph for the solution to $$x \u003e 3$$?

Accepted Answer

A number line with an open circle at $$x = 3$$ and shading to the right.

Question 17

A factory must keep the noise level $$N (in $$decibels) below 85 dB at all times. Which of the following inequalities represents this requirement?

Accepted Answer

$$N \u003c 85$$

Question 18

If $$x is a $$real number such that $$x \geq -4$$ and $$x \u003c 7$$, what is the solution set in interval notation?

Accepted Answer

$$[-4, 7)$$

Question 19

Which of the following is NOT a valid solution set for an inequality?

Accepted Answer

$$(3, 3)$$

Question 20

A water tank must be filled to more than 500 liters but no more than 1200 liters. Which of the following represents the possible volumes $$V in $$interval notation?

Accepted Answer

$$(500, 1200]$$

Solving Linear Inequalities: Concepts, Methods, and Interval Notation

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