Algebra/Chapter 3/Exercises

A set of exercises related to concepts from Chapter 3.

This set contains 9 exercises (including the Conceptual Questions)

Conceptual Questions

Q3.1 (Explaining Equations) In no more than one paragraph, explain in your own words what an "equation" is. In your definition, discuss an equation's purpose, as well as what a solution of an equation means.

Q3.2 (Anatomy of an Equation) Given the statement x + 6 = 12, answer the following.

1. Is this statement true or false?
2. Does x=5 make the statement true?
3. Does x=6 make the statement true?

Q3.3 (Identifying Equations) Determine which of the following are equations.

1. x + 4
2. a - 64 = 45
3. 7 < 8
4. a + 6 > 9
5. 1 + 7 = 8

Q3.4 (Special Solution Sets) Make up an equation whose solution is the null set, and explain why this is the solution set. After this, make up an equation whose solution is the set of all real numbers, and explain why this is the solution set.

Q3.5 (Equivalent Equations) Are the statements 9x + 5 = 4 and 4 = 9x + 5 the same equation? Explain your reasoning.

Exercises

Section 3.1

3.1 (Checking Solutions) Check if the given value(s) is/are solutions to the following equations.

3.2 (Equation Diagrams) Write the equation that best represents the following diagrams.

3.3 (Scales) Look at the diagrams below. How many circles would you need to balance the third scale?

3.4 (Scales) Which is heavier? A red triangle or a blue square?

Section 3.2

3.5 (Finding Inverses) Find the additive and multiplicative inverses of the following numbers.

Section 3.3

3.6 (Solving Equations) Solve the following equations for x.

Section 3.4

3.7 (Oxygen) Approximately 21% of air is oxygen. Using this estimate, determine how many liters of oxygen are in a room containing 25,400 L of air.

3.8 (Triangle) A triangle has a 105 degree angle and a 32 degree angle. What is the measure of its third angle?