CHAPTER 2

SECTION 3 

all hail the mighty multi-step equations!!!

no way. don't even make me laugh (.>_<.)

they are annoying, AND take up too many lines on my paper

that annoys me and I am glad we're done with them already

gah. so, here is my teaching page (.^_^.) enjoy it!

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

a multi-step equation is not really that hard to solve.

you must be able to understand the following terms

when you are working with these math problems.

Distributive property: this is when you multiply a sum

or difference by a number. Such as the following

y = 5(20 - 2x) another way to write this; y = 5(20) - 5(2x)

the end result is this; y = 100 - 10x

Like-terms: terms which are similar to one another.

such as 2x and -5x. they can be combined to make -3x.

EX. combining like-terms

1. Combine like terms

2. Subtract 5 from each side

3. Simplify the equation

4. Divide each side by 3

5. Simplify the equation

- - - - - solve the equation.

a.

5c - 2c + 5 = 26

5c - 2c + 5 = 26

        3c + 5 = 26 

              - 5    - 5

               3c = 21

               3       3

                 c = 7 < --- the final answer

EX. solving an equation with grouping symbols

1. Use the distributive property

2. Add 12 to each side

3. Simplify the equation

4. Divide each side by 2

5. Simplify the equation

- - - - - solve the equation.

a.                         

       2(c - 6) = 100

2(c) + 2(-6) = 100

          2c - 12 = 100

               +12    +12

                  2c = 112

                 2          2

                  c = 56

EX.real-world problem solving

1. Combine like-terms

2. Subtract 45 from each side

3. Simplify the equation

4. Divide by 2 on each side

5. Simplify the equation

- - - - - solve the equation.

length of side + 45 ft + length of side

= amount of fencing

x = length of the side of the walls

across from one another [adjacent]

x + 45ft + x = 100 

2x + 45ft = 100 

- 45      - 45 

2x = 55   

2        2   

x = 27.5

EX. solving with fractions

1. Rewrite the fractions as coefficients

2. Find a common denominator

3. Combine like-terms

4. Multiply each side by the reciprocal

5. Simplify the equation

- - - - - solve the equation.

   2 + 3m = 71

  12   12     12

 2 +  3 m = 71

12   12      12

         5 m = 71

         12      12

          12 * 5 m = 71 * 12 

        5     12      12     5

             m = 355

EX. solving with decimals

1. Multiply each side by 100

2. Use distributive property

3. Simply the equation

4. Subtract 875 from each side

5. Simplify the equation

6. Divide each side by 50

7. Simplify the equation

- - - - - solve the equation

Original -->  0.5a + 8.75 = 13.25

100(0.5a) + 100(8.75) = 100(13.25)

                      50a + 675 = 1325

                              - 675    - 675

                                 50a = 650

                                 50       50

                                     a = 13

[

[[ NOW TRY THESE ON YOUR OWN! ]]

combining like-terms

a.

-x + 4x - 10y + y = 28

b.

20ab - 10b + a - ab / b = 110

c.

72 + 4m - 14c + 7m = 72

solving with grouping symbols

a.

m + 5(m -1) = 7

b.

15 = -3(2w - 1 + 10e)

c.

48 = 8(x + 2)

real world problems

a.

Two friends are renting a house. They pay the first moth's rent,

however the landlord required them to pay an addition half of the

months rent as a security deposit. The total amount paid was $3567.

What is the monthly rent for the house?

b.

A gardener is planting a rectangular garden area in a community

garden. His garden will be next to an existing 45 ft fence. The gardener

has a total of 100 ft of fence to build the other three sides of his garden.

How long will the gardener's garden be if the width is 45 ft?

c.

A carpenter is building a rectangular fence for a school playground.

One side of the playground is the wall the school building which is

100 ft wide. He plans to use 355 ft of fencing material. What is the

length of the playground if the width of it is 100 ft?

solving with fractions

a.

x - 5 = 6

7    7     7

b.

1 + 3d = 4

5     15     5

c.

4 + m = 3

       8      4

solving with decimals 

a.

25.24 + 3.98y = 5

b.

1.12 + 1.24y = 8.62

c.

1.026 + 2.557t = 7.583

WOOHOO I AM FINISHED WITH MY ASSIGNMENT!!

T E E H E E 

TALK ABOUT THE LAST MINUTE KIND OF PERSON