Question

I have just started algebra 1 honors and I need help. Would someone work this out step by step PLEASE
6 + v/-8 = 4/7

Answer 1

You want to isolate the \(v\).

Answer 2

The easiest way to do this is to do the order of operations backwards.

Answer 3

This is because if you multiply and there is still addition remaining, you have to distribute it, and that makes things messy.

Answer 4

So the first step is to subtract

Answer 5

To isolate \(v\) you need \(6\) on the other side. \[
\color{red}6+\frac v{-8}=\frac 47
\]

Answer 6

To do this we need to subtract \(6\) from both sides.

Answer 7

The result is \[
6-6+\frac{v}{-8}=\frac 47-6
\]However the \(6\) cancels out by design and we get: \[
\frac{v}{-8}=\frac 47 -6
\]

Answer 8

The next step is to simplify the right side: \[
\frac 47 -6
\]

Answer 9

We need the denominator to be the same, so we change \(6\): \[
6 = \frac 61 = \frac 61 \times \frac 77=\frac {42}7
\]

Answer 10

Now we can simplify: \[
\frac 47 - \frac {42}7=\frac{4-42}7=\frac{-38}7
\]

Answer 11

Our equation simplified is: \[
\frac{v}{-8}=\frac{-38}{7}
\]

Answer 12

Now let me know if anything confused you so far.

Answer 13

I'm sorry, where did 7/7 come from?

Answer 14

Well, \(7/7 = 1\). So we multiplied \(6\) by \(1\).

Answer 15

This didn't change anything because anything times \(1\) is itself.

Answer 16

Okay, so you know how \(12/3=4\) right?

Answer 17

yes

Answer 18

Well we are doing something similar, but we are going backwards.

Answer 19

We are trying to find a number where: \(??/7=6\)

Answer 20

Because we need \(7\) in the denominator (bottom part) in order to add the fractions.

Answer 21

Does that make sense?

Answer 22

No, sorry

Answer 23

Do you know how to add fractions?

Answer 24

yes

Answer 25

What is: \[
\frac 45 + \frac 28
\]

Answer 26

ok 1 sec

Answer 27

4/5 + 2/8 = + 10/40 +42/40
which equals 1 2/40 or 1 1/20

Answer 28

?

Answer 29

oops, missed a number
32/40 + 10/40 = 42/40 then reduce to simple form

Answer 30

Okay, good.

Answer 31

What is \(\frac 47 - 6\)?

Answer 32

4/7 - 6/1 = 4/7 - 42/7 = -38/7

Answer 33

okay, well if you don't understand what I did, then just understand that: \[
\frac v{-8}=\frac 47-6
\]Simplified to :\[
\frac v{-8}=\frac{-38}7
\]Okay?

Answer 34

ok

Answer 35

Then, to isolate the \(v\), what is left to do?

Answer 36

You need to get rid of \(-8\), so how do you do it?

Answer 37

subtract 1/8 from both sides?

Answer 38

Nope. subtraction is the opposite of addition.

We're dividing. We need the opposite of division.

Answer 39

multiply 1/8 on both sides

Answer 40

Close, but: \[
\frac{v}{-8}\times \frac 18 = \frac{v}{-64}
\]

Answer 41

So we multiply, but multiply by something else.

Answer 42

We want to get \(v\) alone.

Answer 43

I'm stuck

Answer 44

We want to multiply by -8

Answer 45

so would it be -8/1

Answer 46

Yes,

Answer 47

\[
v=\frac{-38}{7}\times \frac{-8}1
\]

Answer 48

so now we get the denominators to match?

Answer 49

-38/7 x -8/1 = -38/7 x -56/7 = 2128/49 = 43.45 (reduced) ???

Answer 50

Wio, are you still here?

Answer 51

Hold on.

Answer 52

What you did is correct.

Answer 53

However, you don't need to make denominators equal when you multiply fractions, so you didn't more work than necessary. it is still correct though.

Answer 54

so when I multiply, I can cross multiple and be done with it?

Answer 55

Wio, THANK YOU SO MUCH!!!!!!!

Answer 56

You found the answer \(v\approx 43.4\)

Answer 57

Thank you again! Have a great night