Question

Create your own two-step equation with All Real Numbers as the solution. Show the steps to solving the equation to prove the solution All Real Numbers.

Answer 1

Still working on this?

an equation will all real numbers as the solution means an equation that is true no matter what number you pick.
Example
x= x
where x is an "unknown" number. Notice that if x is 1, this equation becomes
1=1
which is true... meaning x=1 is a solution.
Of course, it is true no matter what x you pick

Answer 2

hahaha @phi yea i am lol

Answer 3

You now have to make it more complicated
start with
x= x

now multiply and add things to both sides to make it look more complicated.

Answer 4

what "things"? numbers??

Answer 5

like this:
3x = 3x (multiplied both sides by 3)
3x + 4 = 3x + 4 (added 4 to both sides)

we could add letters:
3x + y + 4 = 3x + y + 4 (but we don't want it too complicated)

Answer 6

ok i sort of get that.. how would it be all written out? in answer form?

Answer 7

write down the equation.
solve it.

Answer 8

oh the equation u gave me?

Answer 9

I would feel better if you picked your own equation.

Answer 10

gah! ok lol :P *inner turmoil* >.<

Answer 11

this is so confusing. :/

Answer 12

start with
x= x

now multiply and add things to both sides to make it look more complicated.

Answer 13

start with
x=x
pick a number, and multiply both sides by that number.

Answer 14

ok. im picking a number

Answer 15

5x=5x?

Answer 16

multipy both sides by 5?

Answer 17

now add the same number to both sides (they want a 2-step equation)

Answer 18

5x + 2= 5x+2 ?

Answer 19

where does all real numbers come in? i dont understand what thats supposed to mean

Answer 20

yes, that is an equation.
now "solve it"
which means find all the x values that make that equation true.

Answer 21

oooooooh ok i didnt get that all this time

Answer 22

but now how do i solve it haha??

Answer 23

to solve equations, you simplify them. For example add -2 to both sides, like this
5x + 2 -2 = 5x + 2 - 2
now simplify 2-2 is 0
5x+0 = 5x +0
and 5x+0 is 5x (0 added to anything does not change it)

now you have
5x= 5x

Answer 24

next step: add -5x to both sids

Answer 25

oh like when ur supposed to do the opposite ... to get the answer

Answer 26

yes. but in this case you will end up with
0 = 0

that means the original equation is true for any x value. In other words, it is true for all real numbers.

Answer 27

ok thanks! i figured it out :))

Answer 28

Hopefully your lesson explains this somewheres.

Answer 29

haha but my brain doesnt process it 99.99 % of the time :P

Answer 30

Most of the ideas are not hard... just different so you never thought of them before. If you get stuck, stop and say to yourself "this does make sense... what idea did I miss?"

and ask questions. and don't all asleep.

Answer 31

haha ok thanks