Question 1

Solve the inequality $$9(x - 2) \u003c 2(5x - 1)$$ and write the solution in interval notation.

Accepted Answer

$$(-16, \infty)$$

Question 2

Which property is used when you subtract $$9x$$ from both sides of the inequality $$9x - 18 \u003c 10x - 2$$?

Accepted Answer

Subtraction Property of Inequality

Question 3

What is the first step in solving the inequality $$9(x - 2) \u003c 2(5x - 1)$$?

Accepted Answer

Use the distributive property

Question 4

If the solution to an inequality is $$x \u003e -16$$, how is this written in interval notation?

Accepted Answer

$$(-16, \infty)$$

Question 5

Which of the following best describes the solution set for $$x \u003e -16$$?

Accepted Answer

All real numbers greater than $$-16$$

Question 6

When solving $$-18 \u003c x - 2$$, what is the next step?

Accepted Answer

Add 2 to both sides

Question 7

Which of the following is true about the use of parentheses and brackets in interval notation?

Accepted Answer

Parentheses are used for excluded endpoints

Question 8

A company needs to ensure their product's temperature $$x$$ stays above $$-16$$ degrees Celsius for safety. Which interval represents the safe operating temperatures?

Accepted Answer

$$(-16, \infty)$$

Question 9

If you multiply both sides of an inequality by a negative number, what must you do to the inequality symbol?

Accepted Answer

Reverse the direction of the inequality

Question 10

Which step is NOT necessary when solving $$9(x - 2) \u003c 2(5x - 1)$$?

Accepted Answer

Multiplying both sides by $$-1$$

Question 11

Suppose you have the inequality $$ax + b \u003c cx + d. $$What is the general first step to solve for $$x$$?

Accepted Answer

Move all terms involving $$x to $$one side

Question 12

Which of the following is the correct solution set for $$x \geq -16 in $$interval notation?

Accepted Answer

$$[-16, \infty)$$

Question 13

A medical researcher needs to ensure a dosage $$x is $$always greater than $$-16 mg $$for safety. Which of the following is the correct way to express this requirement?

Accepted Answer

$$x \u003e -16$$

Question 14

If the solution to an inequality is $$x \u003e -16$$, which of the following numbers is in the solution set?

Accepted Answer

$$0$$

Question 15

Which of the following best describes the process of solving a linear inequality?

Accepted Answer

Isolate the variable using properties of inequalities

Solving Linear Inequalities and Writing Solution Sets in Interval Notation

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