Question 1

Which of the following is the correct interval notation for the solution set of the inequality $$x \geq -2$$?

Accepted Answer

$$[-2, \infty)$$

Question 2

Solve the inequality $$2x - 5 \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 6)$$

Question 3

Which property of inequalities must be applied when both sides of an inequality are multiplied or divided by a negative number?

Accepted Answer

The direction of the inequality symbol must be reversed.

Question 4

Graph the solution set of $$-3 \leq x \u003c 2 on a $$number line. Which interval notation represents this set?

Accepted Answer

$$[-3, 2)$$

Question 5

Solve the inequality $$5 - 2x \geq 1$$ and select the correct interval notation for the solution.

Accepted Answer

$$(-\infty, 2)$$

Question 6

Which of the following inequalities has a solution set that is the empty set?

Accepted Answer

$$x + 2 \u003c x - 1$$

Question 7

If $$x$$ must satisfy $$3(x - 2) \u003e 3x + 1$$, what is the solution set?

Accepted Answer

The solution set is empty.

Question 8

A student needs an average of at least 75% in four tests to pass a course. If their first three test scores are 70%, 80%, and 78%, what is the minimum score they must earn on the fourth test to pass?

Accepted Answer

$$72$$

Question 9

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

Accepted Answer

A number line shaded to the right of $$a$$ with a parenthesis at $$a.$$

Question 10

Solve the inequality $$-4(x - 1) \leq 8$$ and express the solution in interval notation.

Accepted Answer

$$[3, \infty)$$

Question 11

Which of the following statements is true about the solution set of $$x + 5 \geq x + 2$$?

Accepted Answer

The solution set is all real numbers.

Question 12

Solve the inequality $$2(x + 4) \u003c 3x + 1$$ and select the correct interval notation for the solution.

Accepted Answer

$$(-\infty, 7)$$

Question 13

Which of the following is the correct set-builder notation for the solution set $$(-\infty, 5]$$?

Accepted Answer

$$\{x | x \leq 5\}$$

Question 14

A chemical reaction must be kept below 120°C to be safe. Which inequality represents the safe temperature range $$T$$?

Accepted Answer

$$T \leq 120$$

Question 15

Solve the inequality $$\frac{1}{2}x - 3 \u003e 5$$ and express the solution in interval notation.

Accepted Answer

$$(16, \infty)$$

Question 16

Which of the following is true about the solution set of $$0 \u003c 1$$?

Accepted Answer

The solution set is all real numbers.

Question 17

A company requires that employees work at least 40 hours per week. Which inequality represents the number of hours $$h an $$employee can work?

Accepted Answer

$$h \geq 40$$

Question 18

Solve the inequality $$-2x + 7 \u003e 1$$ and select the correct interval notation for the solution.

Accepted Answer

$$(-\infty, 3)$$

Question 19

Which of the following is the correct interval notation for all real numbers?

Accepted Answer

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

Question 20

A student’s grades on three exams are 82, 74, and 78. If the final exam counts as two grades, what is the minimum score needed on the final to average at least 80?

Accepted Answer

$$83$$

Linear Equations and Inequalities in One Variable: Study Notes

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