Question

-6(t-7)-(t+8)=2 solve and check the solution t=

Answer 1

Start by expanding all of the brackets. Do you know how to do this?

Answer 2

no

Answer 3

-6t+42-t-8=2
now solve

Answer 4

Let's take the first bracket: -6(t-7)
To expand this we multiply each term inside the brackets by the number outside, and add them together. So we have -6xt=-6t and -6x-7=42. Adding together we have -6t+42. Can you expand the second set of brackets?

Answer 5

t+8

Answer 6

Almost, but notice that the bracket has a - sign in front of it. That means that each term inside the bracket needs to be multiplied by -1 (just change the sign) so -(t+8) just becomes -t-8.
So in all we have -6t+42-t-8=2.
The next step is to collect all of the 'like' terms on the left hand side. (i.e. see how many x's we have and what numbers). Can you do this step?

Answer 7

no

Answer 8

Well, first take the t's. We have -6t -t=(-6-1)t.
What is -6-1?

Answer 9

5

Answer 10

Don't forget the minus sign in front of the 6, the question I asked was:
-6-1
not
6-1
And the answer is?

Answer 11

-5

Answer 12

Not quite, -6-1=-7. Do you see why?

Answer 13

i add 6 and 1 and get 7

Answer 14

Kind of, but the other way round. You subtract 1 from negative 6. So we have figured out that -6-1=-7. Back to the question, we have -6t-1t, so how many t's is that?

Answer 15

2

Answer 16

Ignore the right hand side for now, If I have -6 lots of t and take away another lot of t, then how many lots of t will I have in total? (i.e. -6t -1t)

Answer 17

not sure

Answer 18

7

Answer 19

so would it be t=7

Answer 20

hello

Answer 21

Hi, no that's not right.
We have -6t-t, so in total we have -7t on the left hand side.
Similarly, we have 42-8 on the left hand side as well, which is 34.
So in all on the left hand side we have -7t+34=2.
Now we have to get t on its own to be able to solve it.
First thing to do would be to get rid of that +34 on the left hand side. How would we do that?

Answer 22

not sure

Answer 23

What is the opposite operation of adding 34?

Answer 24

subtracting

Answer 25

Subtracting what?

Answer 26

34-7

Answer 27

What? No, the opposite to adding 34 is subtracting 34, right? Since +34-34=0. Do you understand this?

Answer 28

so 34-34

Answer 29

(Just a reminder that the equation we have now is -7t+34=2)
Subtracting 34 from both sides would indeed get rid of the +34 on the left hand side wouldn't it? Now, if we do the same thing to the right hand side what do we get there?

Answer 30

34-2

Answer 31

Not quite. What did we do to the left hand side?

Answer 32

+34-34

Answer 33

We subtracted 34 right?

Answer 34

ok I am not sure

Answer 35

That's ok. What we had before on the left hand side was -7t+34. But we wanted to get rid of the +34 so that we just had terms involving t, so what we did was to subtract 34 since:
-7t+34-34
=-7t+0
=-7t.
So, if we subtracted 34 from the left hand side, we have to do the same to the right hand side to keep the equation consistent. Do you understand?

Answer 36

so it is 7t

Answer 37

No...the left hand side is equal to -7t. But we substituted 34 from the left hand side, and what we do to one side we have to do to the other. On the right hand side we had 2, so what do we have to do to it?

Answer 38

not sure

Answer 39

We subtracted 34 from the left hand side and we have to do the same to the right hand side, so what do we have to do to the right hand side?

Answer 40

subtract 34 from 8

Answer 41

Where are you getting 8 from?

Answer 42

t+8 I guess I am messing it up

Answer 43

Yes a little bit. Let's step back for a minute. We had:
-7t+34=2
We want to get rid of the +34 on the left so we subtract 34 from both sides, because what we do to one side we have to do to the other as well. So what we get is:
-7t+34-34=2-34
-7t=-32
Does this make sense? The important thing to remember is:
WHATEVER WE DO TO ONE SIDE OF AN EQUATION WE MUST ALSO DO TO THE OTHER SIDE

Answer 44

I put it in capital letters to make sure you understand how important it is, since it's pretty much one of the most important rules in algebra.

Answer 45

ok so what do we do next

Answer 46

we have -7t=-32, so equivilently 7t=32 if we flip the signs on both sides of the equation. Make sense?

Answer 47

ok

Answer 48

So if 7t=32, then how do we find t?

Answer 49

not sure

Answer 50

do we subtract

Answer 51

7-32=25

Answer 52

Not quite. We need t on its own. At the moment it is being multiplied by 7, so we need to do the opposite of this. What is the opposite of multiplying by 7?

Answer 53

dividing by 7 so would it be 7 divided by32

Answer 54

No, you're so close though! You said it right in the first part of your answer. What we need to do to both sides is to DIVIDE BY 7. So on the left hand side, 7t divided by 7 leaves us with y. On the right hand side, we do 32 divided by 7.

Answer 55

i got 4.571428571

Answer 56

Excellent. Now it's probably best to take it to a couple of decimal places, so say t=4.57 (to 2 d.p.)

Answer 57

ok got it