Question 1

Which of the following represents the interval notation for the solution set $$\{ x \mid -3 \u003c x \leq 5 \}$$?

Accepted Answer

$$(-3, 5]$$

Question 2

Given the inequality $$2x - 6 \u003c 0$$, what is the solution in interval notation?

Accepted Answer

$$(-\infty, 3)$$

Question 3

Which of the following correctly expresses the set $$\{ x \mid x \geq 0 \} in $$interval notation?

Accepted Answer

$$[0, \infty)$$

Question 4

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

Accepted Answer

$$[3, \infty)$$

Question 5

Which of the following is the correct interval notation for all real numbers less than or equal to $$7$$?

Accepted Answer

$$(-\infty, 7]$$

Question 6

If $$x$$ satisfies $$0 \u003c x \u003c 5$$, which of the following is the correct interval notation?

Accepted Answer

$$(0, 5)$$

Question 7

Solve the inequality $$-2x \geq 8$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -4]$$

Question 8

Which of the following best describes the solution set for $$x \leq 0 in $$set-builder notation?

Accepted Answer

$$\{ x \mid x \leq 0 \}$$

Question 9

A chemical process is safe only if the temperature $$T is $$between $$14$$ and $$26$$ degrees Celsius, inclusive. Which interval notation represents the safe temperature range?

Accepted Answer

$$[14, 26]$$

Question 10

Solve the inequality $$\frac{1}{4}(x + 2) \geq \frac{1}{12} - \frac{1}{3}x$$ and express the solution in interval notation.

Accepted Answer

$$[12, \infty)$$

Question 11

Which of the following is the correct interval notation for the set $$\{ x \mid x \u003e 0 \}$$?

Accepted Answer

$$(0, \infty)$$

Question 12

A medication is effective for blood pressure values $$x$$ such that $$114 \leq x \u003c 126. $$Which interval notation represents the effective range?

Accepted Answer

$$[114, 126)$$

Question 13

Solve the inequality $$2x + 12 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3.5, \infty)$$

Question 14

Which of the following is the correct interval notation for the set $$\{ x \mid x \leq 7 \}$$?

Accepted Answer

$$(-\infty, 7]$$

Question 15

Solve the inequality $$\frac{5}{3}(x + 1) \geq \frac{5}{3}(3 + 2x)$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 2]$$

Question 16

A company only hires applicants aged between $$18$$ and $$65$$, inclusive. Which interval notation represents the eligible age range?

Accepted Answer

$$[18, 65]$$

Question 17

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

Accepted Answer

$$(-\infty, 0)$$

Question 18

Solve the inequality $$3x - 7 \leq 2x + 5$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, 12]$$

Question 19

Which of the following is the correct interval notation for the set $$\{ x \mid x \geq -2 \}$$?

Accepted Answer

$$[-2, \infty)$$

Question 20

A water filter is effective for pH values $$x$$ such that $$6 \u003c x \leq 8. $$Which interval notation represents the effective pH range?

Accepted Answer

$$(6, 8]$$

Interval Notation and Solving Linear Inequalities

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