Question

Hello I just needed someone's help on my PRE-ALG
Questions
2(x-3) = 2x
1.one solution
2.no solution
3. infinitely many solutions

2. 3(y - 3) = 2y - 9 + y

1. one solution
2. no solutions
3. infinitely many solutions

3. 10x - 2 - 6x = 3x - 2 + x

1. one solution
2. no solutions
3. infinitely many solutions

4. 4(x + 3) + 2x = x - 8

1. one solution
2. no solution
3. infinitely many solutions

Answer 1

Hi what exactly are you stuck with?

Answer 2

I have problem with understanding it

Answer 3

Ok, so do you know what "having a solution" is?

Answer 4

yeah

Answer 5

the first 3 have no solutions n the last has one solution
coz in the first 3 equations when u solve it the x gets cancelled

Answer 6

when u simplify the first equation both sides have 2x so it gets cancelled
same wid the next 2 equations but only in the last one u get one solution

Answer 7

the first one has no solution, while the second and the third one have infinite amount of solutions. The last one has one solution.

Answer 8

o ok i see

Answer 9

The reason for the first one having no solution is because when you divide both sides by two:

\[\frac{2(x-3) }{ 2 }=\frac{ 2x }{2 }\]

you get

x-3 = x

which we know is false, because x-3 does not equal x. Therefore there is no solution for this.

Answer 10

wait y the second and third have infinite solutions?

Answer 11

o i see now i was doing it wrong the whole time lol thank you on my other tests

Answer 12

However, for the second and third one, through simplification of the equations, we have:

2) 3y-9 = 3y -9
3) 4x-2 = 4x-2

Notice how the functions on both sides of the equal sign are the same. This means that both functions will overlap each other entirely when graphed. They will always equal to each other.

Answer 13

i took the first one as
\[2x-6=2x\]
\[-6=0\]
which isnt possible so 0 solutions

Answer 14

i still didnt get the reason for second and third equations having infinite solutions

Answer 15

Ok. Looking at this graphically, "having a solution" means that both functions will cross each other (aka the values of both functions will equal at some point). Having one solution means the value of both functions will equal at one point. Having no solution means the values of both functions will never equal. Having an infinite amount of solutions means that the values of both functions will always equal to each other.

Given that for #2 and #3, we have an identical function on each side of the equal sign, they will always equal to each other. So they will always overlap each other graphically.

Answer 16

thanks for both of your help.

Answer 17

oh thnx for explaining

Answer 18

no probs