Question 1

Solve the inequality $$5x \u003c 4x + 2$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2)$$

Question 2

Which property allows you to subtract the same value from both sides of an inequality without changing its solution set?

Accepted Answer

Addition property of inequality

Question 3

Given the inequality $$x \u003c 2$$, which of the following is the correct graph representation?

Accepted Answer

A number line shaded to the left of 2 with an open circle at 2

Question 4

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

Accepted Answer

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

Question 5

Which interval notation represents all real numbers less than but not including 5?

Accepted Answer

$$(-\infty, 5)$$

Question 6

A chemical process is safe if the temperature $$T (in$$ °C) satisfies $$T \u003c 120. $$Which is the correct interval notation for the safe temperature range?

Accepted Answer

$$(-\infty, 120)$$

Question 7

Which of the following statements about interval notation is correct?

Accepted Answer

A parenthesis means the endpoint is not included.

Question 8

Solve the inequality $$7x - 3 \u003c 4x + 6$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 3)$$

Question 9

A medication is effective for patients whose age $$a$$ satisfies $$a \u003c 65. $$Which of the following is the correct set notation for eligible patients?

Accepted Answer

$$\{a \mid a \u003c 65\}$$

Question 10

If $$x \u003c 2$$, which of the following values of $$x is $$NOT in the solution set?

Accepted Answer

$$2$$

Question 11

Which of the following is the correct interval notation for the solution set of $$x \u003e -4$$?

Accepted Answer

$$(-4, \infty)$$

Question 12

A historical event occurred before the year 1900. Which interval notation represents all years $$y$$ before 1900?

Accepted Answer

$$(-\infty, 1900)$$

Question 13

Which of the following is NOT a valid interval notation for a solution set?

Accepted Answer

$$(4, 4)$$

Question 14

If $$x \u003c 2$$, which of the following is the correct set-builder notation for the solution set?

Accepted Answer

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

Question 15

A company only hires applicants with experience $$e (in $$years) such that $$e \geq 3. $$Which interval notation represents eligible applicants?

Accepted Answer

$$[3, \infty)$$

Solving Linear Inequalities and Expressing Solutions in Interval Notation

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