3 Title

Beginning Algebra
Tutorial 4: Introduction to Variable Expressions and Equations

 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

 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

 *Inside absolute value       *Exponent *Add num and subtract den.   *Simplify fraction

 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

 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.

 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.

Last revised on July 24, 2011 by Kim Seward.