Question 1

Which property of inequalities requires you to reverse the direction of the inequality when dividing both sides by a negative number?

Accepted Answer

Multiplication property of inequality

Question 2

Solve the inequality $$-5x \leq 20$$ and express the solution in interval notation.

Accepted Answer

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

Question 3

What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?

Accepted Answer

The inequality sign reverses direction

Question 4

Given the inequality $$6x \u003e -18$$, what is the solution in interval notation?

Accepted Answer

$$(-3, \infty)$$

Question 5

If $$x \u003c a$$, how should you shade the number line?

Accepted Answer

Shade to the left of $$a$$

Question 6

Which interval notation correctly represents the solution set for $$x \leq 5$$?

Accepted Answer

$$(-\infty, 5]$$

Question 7

A chemical reaction requires the temperature $$T to be at $$least $$-20$$ degrees Celsius. Which interval notation represents the possible values for $$T$$?

Accepted Answer

$$[-20, \infty)$$

Question 8

Solve the inequality $$-3x \u003e 12$$ and select the correct interval notation for the solution.

Accepted Answer

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

Question 9

A medical dosage must not exceed $$50 mg. $$Which inequality and interval notation correctly represent this restriction?

Accepted Answer

$$x \leq 50$$, $$(-\infty, 50]$$

Question 10

Which of the following is the correct solution to the inequality $$4x + 8 \geq 0$$?

Accepted Answer

$$x \geq -2$$

Question 11

A historical event occurred before the year $$2000. $$Which inequality and interval notation represent all possible years?

Accepted Answer

$$x \u003c 2000$$, $$(-\infty, 2000)$$

Question 12

Solve the inequality $$7x - 21 \u003c 0$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, 3)$$

Question 13

If $$x \geq a$$, how should you shade the number line?

Accepted Answer

Shade to the right of $$a$$

Question 14

Which of the following is the correct interval notation for the solution set of $$x \u003e -7$$?

Accepted Answer

$$(-7, \infty)$$

Question 15

A factory must keep its emissions below $$100$$ units. Which inequality and interval notation represent this requirement?

Accepted Answer

$$x \u003c 100$$, $$(-\infty, 100)$$

Question 16

Solve the inequality $$-2x \leq 10$$ and write the solution in interval notation.

Accepted Answer

$$(-\infty, -5]$$

Question 17

Which of the following statements is TRUE about the solution set for $$x \leq -9$$?

Accepted Answer

The solution includes $$-9$$ and all numbers less than $$-9$$

Question 18

A student must score at least $$70 to $$pass an exam. Which inequality and interval notation represent the passing scores?

Accepted Answer

$$x \geq 70$$, $$[70, \infty)$$

Question 19

Which of the following is the correct solution to the inequality $$-8x \leq 72$$?

Accepted Answer

$$x \leq -9$$

Solving Linear Inequalities and Graphing Solution Sets

Study Guide - Practice Questions

Study Guide - Flashcards