Beginning Algebra
Answer/Discussion to Practice Problems
Tutorial 4: Introduction to Variable Expressions and Equations

WTAMU > Virtual Math Lab > Beginning Algebra > Tutorial 4: 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

(return to problem 1a)

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

(return to problem 1b)

Answer/Discussion to 2a

*Inside ( )

*Multiply
*Add

(return to problem 2a)

Answer/Discussion to 2b

*Inside absolute value

*Exponent

*Add num and subtract den.

*Simplify fraction

(return to problem 2b)

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

(return to problem 3a)

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.

(return to problem 4a)

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.

(return to problem 4b)

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

(return to problem 5a)

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!!!

Putting everything together we can translate the given english phrase with the following algebraic expression:

The product of 12 and a number

(return to problem 5b)

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

(return to problem 6a)

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.

(return to problem 6b)

WTAMU > Virtual Math Lab >Beginning Algebra >Tutorial 4: Introduction to Variable Expressions and Equations