Question

Equations with infinite and no solutions:
Solve each equation:
1) 6x+3-6x=3

Answer 1

My daughter put infinite... is that correct?

Answer 2

If there are infinitely many solutions, can you list a few of them ?

Answer 3

I dont even know what to do lol

Answer 4

You're given an equation

Answer 5

well the 6x cancels out when you combine them and so does the 3

Answer 6

A "number" is called a solution to an equation if you get a "true" statement when you plugin the "number" into the equation

Answer 7

6x+3-6x=3

Answer 8

maybe plugin x = 1 and see if "1" is a solution

Answer 9

6*1+3-6*1 = 3

6 + 3 - 6 = 3

3 = 3

which is true, therefore 1 is a solution to the given equation

Answer 10

so you just have to keep trying numbers

Answer 11

Nope, I have just given you an example to explain what is a solution

Answer 12

6x+3-6x=3

cancelling 6x both sides gives you
3 = 3

which is true no matter what x is.
therefore "every number x" is a solution to the given equaiton

Answer 13

so that means it has to be infinite?

Answer 14

Yep, there are infinitely many numbers

Answer 15

so for instance 0=-4p+4p if you plug in 1 for both it still equals 0 so infintie?

Answer 16

Exactly! If you plugin 1 or 2 or 3 or anything for p, you still get a true statement : 0 = 0

therefore all numbers are solutions to above equation

Answer 17

ok what about a-a=-5

Answer 18

its no

Answer 19

a-a = -5

0 = -5

which is FALSE no matter what "a" is.
Therefore there are NO solutions to the given equation

Answer 20

In other words, you can never find a value for "a" that satisfies above equation

Answer 21

ok great so i can try to plug in 1 for everything and if it doesnt work then there are none

Answer 22

and if it does there is infinite

Answer 23

not so simple, you need to convince yourself that there are indeed infinitely many solutions

Answer 24

But yeah, what you said works..