Solving basic algebra problems- unwrapping the package to ...



Solving basic algebra problems- unwrapping the package to see what

is inside the box.......

When you wrap a present, such as For your cousin or friend to find

a bracelet, for a cousin or friend, out what is in the box, they have to

you

1. wrap the bracelet in tissue paper 6. unwrap the tissue paper

2. put the bracelet into a box tape 5. take out the bracelet

3. close the box 4. open the box

4. wrap the box in wrapping paper 3. unwrap the box

5. tape the paper together 2. take off the tape

6. tie ribbon around the box 1. untie the ribbon

There are two “rules” for finding out what is in the box – you have to do

things in the reverse order, and you have to do the opposite thing at each

step. Those exact same rules work for basic algebra problems – all you

are doing is unwrapping the package, step by step, and doing the opposite thing at each step.

So how does this work?

When you do a calculation, such as 3 x 4 + 8 [pic] 2, you use BEDMAS (Brackets, then exponents, division or multiplication, addition or division)

and do multiplication and division before you do addition so

3 x 4 + 8 [pic] 2 = 12 + 4

= 16

The reverse order for solving an equation is --- SAMDEB!

And the opposite operations are addition is opposite to subtraction

multiplication is opposite to division

square root is opposite to square

So lets solve a pretty standard type of problem:

7x – 5 = 29 SAMDEB says we have to undo the subtraction first

+5 +5 by doing the opposite thing to both sides eg. +5

7x + 0 = 34

7x = 34

Now we have to undo the multiplication by 7, and

the opposite is to do a division by 7

[pic] = [pic] but [pic] = 1 so

1x = [pic] or

x = 4[pic]

Notice that - there should be an x (or other letter) in each line,

there should be one “=” in each line

34[pic] 7 is written as the fraction form, [pic]

Here’s another one:

[pic] + 3 = 9.2 undo the addtion of 3 first

[pic] + 3 = 9.2 the opposite is subtraction

-3 -3

[pic] +0 = 6.2

[pic] = 6.2 now undo the division of x by 2

2 x [pic] = 2 x 6.2

[pic] = 12.4 but 2 [pic] 2 is 1

1x = 12.4 or

x = 12.4

In effect, what you are doing is ending up by moving a number to the

other side of the “=” sign and changing the operation to the opposite one, and some people like to think of it this way – like picking the number up and physically moving it across the “=” and changing the operation. You can actually do this with bits of paper, if it helps think out a problem.

try 5 – 2x = 18 cover up the 5 with your finger to see how to

start the next line,

then move the 5 across and make it – 5

- 2x = 18 – 5 (notice the “-“ stays on the 2x)

- 2x = 13

now “pick up” the –2, a multiplier, and move it

across to make it a divisor

x = [pic] or

x = -6[pic]

So you only need 2 rules for solving basic algebra equations:

1. SAMDEB is the order in which you unwrap the box

2. unwrap a step by doing the opposite operation to the one that is there.

Rules:1. SAMDEB is the order to undo things.

2. Undo things by doing the opposite to both sides

And remember,

x or letter in each step,

“=” in each step

show division in fraction form

Example:

4x –2 = 15 undo –2 with +2

4x –2 = 15

+2 +2

4x = 17 now undo mult by 4

by dividing by 4

[pic] = [pic]

x = 4[pic]

You complete this one:

[pic] + 3 = 8 undo the +3 by____

[pic] +3 = 8

___ ___

[pic] = ____ now undo division by 2

2 [pic] [pic] = 2 [pic]_____

x = 10

Do the following problems, showing your working carefully in steps

1. 3x – 4 = 17

3x =

3x = __

x =

2. x + 5 = 16

3

x =

3

[pic]x = [pic]

3

x =

3. 2x + 6 = 18

=

=

x =

4. 4x – 1 = 16

=

=

x =

5. [pic] - 1 = 16

=

=

x =

6. [pic] = 7 (hint: get rid

of the divisor first)

=

=

x =

7. 2x – 6 = 487

=

=

x =

8. 9x + 5 = 104

=

=

x =

9. [pic] + 3 = 21

=

=

x =

10. [pic] - 4 = 7

=

=

=

x =

11. 5 – 3x = 28

-3x =

=

x =

12. 8x – 16 = 47

=

=

x =

13. 3x + 4 = 27

=

=

x =

14. 25x – 4x = 15 (hint: simplify first)

=

=

x =

15. 4x + 5 – 2x = 6

=

=

=

x =

16. [pic] + 8 = 17

=

=

x =

17. 42x – 3 ½ = 15

=

=

x =

18.[pic]- 4 = 2

=

=

=

x =

19. 25 – 5x = 8

=

=

x =

20. 6a + 5 = 10

=

=

a =

21. 15a + 42 = 82

=

=

a =

22. x – 1039 = - 942

=

x =

23. x + 334 = - 67

=

x =

24. 5x – 18 + 5x = 23

=

=

=

x =

25. 5 - [pic] = 8

=

=

x =

Now check your answers yourself: put each answer for x back into the equation and use BEDMAS to see if the number works as it should.

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