Question

solve for x...but how?
(x-7)/5 + 1/5 = -x/10

Answer 1

If you add +x/10 to both sides, what do you get?

Answer 2

everything to the left and it equally 0

Answer 3

if we write it out:
(x-7)/5 + x/10 +1/5=0

we could do a couple of things. one way:
we have fractions. find the common denominator (it is 10)

or, another way. If we multiply everything (both sides, all terms) by 10, we can make the denominators go away.
which way do you want to go?

Answer 4

Both ways are really the same thing, or at least, get us to the same place.

Answer 5

make the denominators go away

Answer 6

so multiply both sides by 10:
10*( (x-7)/5 + x/10 +1/5 ) = 10*0

distribute the 10 (that means multiply 10 times each term inside the parens)
what do you get?

Answer 7

10x-70/50 + 10/50 = -10/-100

Answer 8

-10x/-100

Answer 9

I'll do the first term
\[ 10\cdot \frac{(x-7)}{5}= 2(x-7) \]
divide the 5 into the 10 to get 2

Answer 10

pretty close, but when you multiply by 10 you are multiplying by 10 not 10/10
do it the way I just posted.

Answer 11

okay

Answer 12

what did you get?

Answer 13

10x-70/50 = 2x-14

Answer 14

pay attention:

we start with
10*( (x-7)/5 + x/10 +1/5 ) = 10*0

don't think too hard. just multiply 10 times each term (that means write 10* next to each term) like this:

10*(x-7)/5 + 10*x/10 + 10*1/5= 10* 0

now divide the bottom into the top
can you do that ?

Answer 15

i really dont get what youre saying

Answer 16

i dont understand how you got 10 times 0

Answer 17

remember we started with
(x-7)/5 + x/10 +1/5=0

then we multiply BOTH SIDES by 10
because that is what we have to do to keep things equal. If you multiply 10 times the left side, you do the same to the right (to be fair!)

so we write down
10*( (x-7)/5 + x/10 +1/5 ) = 10*0

now on the right side, 10*0 is 0 right?
and on the left, it is
10*(x-7)/5 + 10*x/10 + 10*1/5= 0

Answer 18

yes i understand now

Answer 19

now you should learn this
10*(x-7)/5 can be simplified by dividing 5 into 10 to get 2. we can re-write it as
2*(x-7)

can you do the other two terms?

Answer 20

10*x/10

Answer 21

x

Answer 22

2(x-7)+x+2

Answer 23

yes, now the last one
10*1/5

Answer 24

2

Answer 25

ok, you went too fast. so you got
2(x-7)+x+2 = 0 (don't leave out the = 0, they are important)

can you distribute the 2 (multiply 2 times each term inside the parens)

Answer 26

2x-14+x+2=0

Answer 27

yes. now 2x+1x is ?

Answer 28

3x

Answer 29

and -14+2 is ?

Answer 30

-12.... i get it now x-4

Answer 31

?

Answer 32

huh....it's 2x+x=12
then 3x=12
x=4

Answer 33

yes. That is how you solve it.

Answer 34

thank you

Answer 35

we can check it, by replacing x with 4 in
(x-7)/5 + 1/5 = -x/10

(4-7)/5 + 1/5= -4/10

(4-7) is -3, so

-3/5 +1/5 = -4/10
-2/5 = -4/10
simplify the right side by dividing the top by 2 and the bottom by 2
-2/5 = -2/5
it worked.

Good job.

Answer 36

yes...thank you!

Answer 37

(x-7)/5 + 1/5 = -x/10

Given:

\(\large\frac{x-7}{5} + \frac{1}{5} = -\frac{x}{10}\)

Combine fractions on the left side to get:

\(\large\frac{x - 6}{5} = -\frac{x}{10}\)

Cross Multiply to get:
\(10(x-6) = -5x\)

Distribute the 10 across (x-6) to get:
10x - 60 = -5x

Add 5x to both sides; add 60 to both sides:

10x + 5x = 60

Simply the left side:

15x = 60

Divide both sides by 15

x = 4