Beginning Algebra
Answer/Discussion to Practice
Problems
on Introduction to Variable
Expressions
and Equations
 Answer/Discussion
to 1a
|
| In this problem, what is the base?
If you said 2, you are correct!
What is the exponent?
If you said 5, you are right!
Let's rewrite it as multiplication and see what we get for an answer: |
 |
*Rewrite the base 2, five times in a product
*Multiply |
| Answer/Discussion
to 1b
|
| In this problem, what is the base?
If you said 1/6, you are correct!
What is the exponent?
If you said 3, you are right!
Let's rewrite it as multiplication and see what we get for an answer: |
 |
*Rewrite the base 1/6, three times in a product
*Multiply |
| Answer/Discussion
to 2a
|
 |
*Inside ( )
*Multiply
*Add |
| Answer/Discussion
to 2b
|
 |
*Inside absolute value
*Exponent
*Add num and subtract den.
*Simplify fraction
|
| Answer/Discussion
to 3a
|
| Plugging in the corresponding value for each variable and then evaluating
the expression we get: |
 |
*Plug in 1 for
x, 2 for y, and 3 for z
*Inside parenthesis
*Exponent in [ ]
*Add in [ ]
*Multiply |
| Answer/Discussion
to 4a
|
| Replacing x with
0 we get: |
 |
*Plug in 0 for x
*Evaluate both sides |
| Is 0 a solution?
Since we got a FALSE statement (7 does not equal 9), then 0
is not a solution. |
| Answer/Discussion
to 4b
|
| Replacing x with
8 we get: |
 |
*Plug in 8 for x
*Evaluate both sides |
| Is 8 a solution?
Since we got a TRUE statement (6 does equal 6), then 8 is
a solution. |
| Answer/Discussion
to 5a
9 less than 5 times a number. |
| What operation will we replace less than with?
If you said subtraction you are correct!!!
What operation will we replace times with?
If you said multiplication you are correct!!!
The phrase 'a number' indicates that it is an unknown number.
There was no specific value given to it. So we will replace
the phrase 'a number' with the variable x.
We want to let our variable represent any number that is unknown
Putting everything together we can translate the given english phrase
with the following algebraic expression:
9 less than 5 times a number
|
| Answer/Discussion
to 5b
The product of 12 and a number. |
| What operation will we replace product with?
If you said multiplication you are correct!!!
The phrase 'a number' indicates that it is an unknown number.
There was no specific value given to it. So we will replace
the phrase 'a number' with the variable x.
We want to let our variable represent any number that is unknown
Putting everything together we can translate the given english phrase
with the following algebraic expression:
The product of 12 and a number
|
| Answer/Discussion
to 6a
The sum of 10 and 4 times a number is the same as 18. |
| Do you remember what sum translates into?
If you said addition, you are doing great.
Do you remember what times translates into?
If you said multiplication, you are doing great.
'Is the same as' will be replaced by the symbol =.
Let's put together everything going left to right:
The sum of 10 and 4 times a number is the same as 18
|
| Answer/Discussion
to 6b
The quotient of a number and 9 is 1/3. |
| Do you remember what quotient translates into?
If you said division, you are correct.
'Is' will be replaced by the symbol =.
Let's put together everything going left to right:
The quotient of a number and 9 is 1/3.
|
All contents copyright (C) 2001 - 2008, WTAMU and Kim Seward. All rights reserved.
Last revised on Jan. 8, 2002 by Kim Seward. |
