Question

-(z+7)+(3z+1)=-5(z+1)
the solution to the set is z=

Answer 1

@ConDawg @GoldPhenoix @whpalmer4

Answer 2

\[-(z+7)+(3z+1) = -5(z+1)\]apply distributive property
\[-z-7 + 3z + 1 = -5z -5\]collect like terms
\[2z-6 = -5z -5\]solve for \(z\)

Answer 3

@whpalmer4 thats what i got as far as the 2z-6 but i dont understand anything else

Answer 4

Okay, why don't you add 5z to both sides, what do you get?

Answer 5

what 1z

Answer 6

i mean 3z

Answer 7

@whpalmer4

Answer 8

huh? write out the equation, and add +5z on each side of the equals sign. what do you get?

Answer 9

2z-6=5z-5
5z 5z
3z-6=0-5

Answer 10

@whpalmer4 idk?

Answer 11

@whpalmer4 Did most of the work for you here.

Answer 12

\[2z-6=-5z-5\]

Answer 13

You want you variables on one side and constants on the other. You can do that right?

Answer 14

so is the solution 2z-6?

Answer 15

No. Right now we have 2z-6=-5z-5.
We need to know the value of just z.
2z-6=-5z-5 doesn't give us that value of z

But we can change the equation 2z-6=-5z-5 to give us the value of z
All you need to do is get the z's on one side of the equal sign and constants on the other

Answer 16

or is it 0.1428571429

Answer 17

well lets see

Answer 18

2z-6=-5z-5

2z=-5z+1

7z=1

z= 1/7

1/7 = 0.1428571429

But it's better to use 1/7

Answer 19

y is that @ConDawg

Answer 20

Why is it better to use 1/7?

Answer 21

right

Answer 22

Because it's a nice fraction, and is just better to look at then 0.1428571429

Answer 23

ok now i c @ConDawg

Answer 24

:)

Answer 25

sorry, had some technical difficulties.

what I was trying to show you, @Avon, was

\[2z-6=-5z-5\]We add \(5z\) to each side
\[2z-6+5z = -5z - 5 + 5z\]now collect like terms
\[7z - 6 = -5\]Now add 6 to each side
\[7z - 6 + 6 = -5 + 6\]collect like terms
\[7z = 1\]now divide each side by 7 to get \(z\) all alone
\[7z/7 = 1/7\]\[z=1/7\]

Answer 26

as long as we do the same thing to both sides of the equation, it remains true.

if you and your friend both have $10, you both have the same amount of money. If someone comes along and gives each of you another $20 bill, you both have the same amount of money, even though the amount is now different than what it was originally.