Math 6A ( Periods 2 & 7)

Adding & Subtracting Linear Expressions 13.2

A linear Expression is an algebraic expression in which the
exponent of the variable is 1.

Linear expressions include:  -4x,  3x + 5   5 – x/2

Nonlinear Expressions include:  x2,  -7x³ + x,    x⁵ + 1

ADDING LINEAR EXPRESSIONS

There are two methods for adding linear expression

Vertical and Horizontal methods

Vertical Method

(x -2) + (3x +8)

Align like terms vertically and add

 

Horizontal Method

Use properties of operation to group like terms and then simplify

(-4y +3) + (11y -5)

= -4y + 3 + 11y + - 5

= -4y + 11y + 3 + -5    Use Commutative Property of Addition and Group  LIKE TERMS

= 7y – 2                      Combine LIKE TERMS

Find  2(-7.5z + 3)  + ( 5z – 2)

Use the DP      -15z + 6 + 5z + -2

Commutative Property of Addition    -15z + 5z + 6 + -2

Combine like terms    -10z + 4

SUBTRACTING LINEAR EXPRESSIONS

To subtract one linear expression from the other, add the opposite of each term in the expression. You can use either the vertical or horizontal methods; however,  I find the vertical method works the best

(5x + 6 )  - (-x + 6)

so it simplifies to just

6x

(7y + 5)  -2(4y-3) = 7y + 5 -8y + 6 Use the DP

=7y -8y + 5 + 6  ( Using the C+)

-y + 11

REAL LIFE APPLICATION

The original price of a cowboy hat is  d dollars. You use a coupon and buy that hat for
( d - 2) dollars. You decorate the hat and sell it for ( 2d – 4) dollars. Write an expression that represents your earnings from buying and selling the hat. Interpret that expression.

Earnings = selling price – purchase price

Earnings = ( 2d – 4)  - ( d – 2)

Write it as a sum—ADD THE OPPOSITE and Use the DP to distribute the negative

2d – 4 + -d + 2

Group like terms

2d – d + -4 + 2

Combine like terms

d – 2

You earn ( d - 2) dollars. You also paid ( d -2) dollars so you doubled your money by selling the hat for twice as much as you [aid for it!

GEOMETRY The expression 17n + 11 represents the perimeter ( in feet) of this triangle.  Write an expression that represents the third side

 

17n+ 11 – ( 5n + 6 + 4n + 5) = the third side

One way:

Combine like terms within the parenthesis first

17n + 11  - ( 9n + 11)

Distribute the negative
17n + 11 – 9n -11

combine like terms

8n

The third side would be 8n feet

FACTORING EXPRESSIONS

When factoring expressions you write the expression as a product of factors.

Factor

24x -18 using the GCF

Find the GCF of 24 and 18

OMG—use the box method or write their prime factorization

The GCF is 6

Rewrite

24x – 18  as

6(4x) – 6(3)

Use the DP

6(4x -3)

so

24x – 18 = 6(4x -3)

Try 15w + 65

The GCF = 5

5(3w) + 5(13)

5(3w + 13)

How about 21m – 49n

The GCF = 7

7(3m) – 7(7n)

7(3m -7n)

Factoring out a Fraction

Factor ½ out of

Write each term as the product of ½ and another factor

Use the DP to factor out ½