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Math 0308: Introductory Algebra
Instructor: Jennifer Travis
Journal Assignment 2
Journal responses should be completed in a composition notebook with a
cardboard cover, like the one pictured. Do not turn in loose or stapled pages.
Write only on the front of the pages.
It is not necessary to copy all the prompts/questions into your journal, but you
should label your response with the prompt/question number. However, your
journal will be more helpful to you if you either paraphrase/summarize the
prompt, or if you print the journal assignment, cut it up, and tape the
prompts/questions into your journal.
All responses are expected to be college level work, using complete sentences and appropriate
mathematical vocabulary. You must provide meaningful responses to all of the questions/prompts in
the assignment.
For yes/no questions, you must explain the reasons for your response.
1. Explain the difference between an algebraic expression and an equation.
2. Explain the difference between “solving” and “simplifying”, and give an example of each.
3. What does it mean for two equations to be equivalent?
4. When simplifying an expression, should equals signs be used? If so, give a correct example of
their use.
5. Suppose a student solved an equation using the following steps:
3x  1  4 x  3
3x  1  4 x  3  1
3x  4 x  4
3x  4 x  4 x  4
1x  4
1  1
x4
Critique this solution process. Explain any errors you find. For the solution process to be
correct, not only must the final answer be correct, but each step must follow logically from the
previous step. When solving an equation, each line should contain an equation that is
equivalent to the original equation.
6. Students are often told to “move a term to the other side of the equation.” Is this advice correct?
Why or why not? Explain the correct way to “move a term to the other side of the equation.”
Page 2 of 2
Math 0308: Introductory Algebra
Instructor: Jennifer Travis
Journal Assignment 2
7. You may have heard of the mnemonic device PEMDAS, or “Please Excuse My Dear Aunt
Sally,” for remembering the order of operations. (PEMDAS: Parentheses, Exponents,
Multiplication, Division, Addition, Subtraction).
Suppose a student solved an equation using the following steps:
3(2 x  3  4 x  2)  3(5 x)  7  2
6 x  9  12 x  6  3(5 x)  5
18 x  15  3(5 x)  5
18 x  3(5 x)  10
18 x  15 x  10
3x  10
10
x
3
10 
Solution Set:  
3
Are there any errors in this solution process? Is the final answer correct? Did this person
follow PEMDAS? If the person did not follow PEMDAS but did not make any errors, explain
why it was acceptable to do the operations in a different order.
8. Provide an example of an equation that has {0} for its solution set. Your example should have
at least two terms on each side of the equation. Write out a correct solution process for the
equation. Do NOT use a problem from the book or notes—make up your own.
9. Provide an example of an equation that has no solution. Your example should have at least two
terms on each side of the equation. Write out a correct solution process for the equation. Do
NOT use a problem from the book or notes—make up your own.
10. Provide an example of an equation in which the solution set is All Real Numbers. Your
example should have at least two terms on each side of the equation. Write out a correct
solution process for the equation. Do NOT use a problem from the book or notes—make up
your own.
11. Explain how to recognize when an equation has no solution, or when the solution set is All
Real Numbers.
12. Under what circumstances do we reverse the direction of an inequality sign? Why must we do
this?
13. Suppose a student solves an inequality and obtains 4  x . Explain to the student how and why
they should rewrite this inequality, before attempting to graph it on a number line.