Question 1

Which of the following represents the interval of all real numbers $$x$$ such that $$2 \u003c x \leq 7 in $$interval notation?

Accepted Answer

$$(2,7]$$

Question 2

What is the intersection of the intervals $$[1,5]$$ and $$(3,8)$$?

Accepted Answer

$$(3,5]$$

Question 3

Solve the inequality $$5x - 7 \u003c 18. $$Express your answer in interval notation.

Accepted Answer

Question 4

Which of the following is the solution set for the compound inequality $$-2 \u003c x + 1 \leq 4$$?

Accepted Answer

$$(-3,3]$$

Question 5

Solve the absolute value inequality $$|x - 2| \u003c 5. $$Express your answer in interval notation.

Accepted Answer

$$(-3,7)$$

Question 6

Which of the following intervals represents all real numbers except $$x = 4$$?

Accepted Answer

$$(-\infty,4) \cup (4,\infty)$$

Question 7

A chemical process is safe only if the temperature $$T (in $$degrees Celsius) satisfies $$15 \leq T \u003c 80. $$Which interval notation correctly describes the safe temperature range?

Accepted Answer

$$[15,80)$$

Question 8

Solve the inequality $$-3x + 9 \geq 0$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty,3]$$

Question 9

Which of the following is the union of the intervals $$(-\infty,2]$$ and $$[1,5)$$?

Accepted Answer

$$(-\infty,5)$$

Question 10

Solve the absolute value inequality $$|2x + 1| \geq 7$$ and express your answer in interval notation.

Accepted Answer

$$(-\infty, -4] \cup [3, \infty)$$

Question 11

A medical test is valid only if the patient's blood pressure $$P$$ satisfies $$90 \u003c P \leq 120. $$Which of the following is the correct interval notation for valid blood pressure readings?

Accepted Answer

$$(90,120]$$

Question 12

Which of the following inequalities has no solution?

Accepted Answer

$$|x| \u003c 0$$

Question 13

Solve the compound inequality $$2x - 1 \u003e 3$$ and $$x + 4 \u003c 10. $$Express your answer in interval notation.

Accepted Answer

$$(2,6)$$

Question 14

Which of the following is the correct solution set for $$|x + 3| \leq 2$$?

Accepted Answer

$$[-5,-1]$$

Question 15

If $$x$$ must satisfy both $$x \u003e -2$$ and $$x \leq 5$$, which interval notation represents all possible values of $$x$$?

Accepted Answer

$$(-2,5]$$

Linear Inequalities and Absolute Value Inequalities – Study Notes

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