Question

Please help me understand, i dont want answers.. I will medal and fan!!
Solve for x: 2 over 3 (x − 2) = 4x.

negative 2 over 5
negative 5 over 2
2 over 5
5

Answer 1

I am horrible at fractions, so any help would be great..

Answer 2

Do you mean:

\(\dfrac{2}{3}(x - 2) = 4x\)

Answer 3

yes ma'am/ sir

Answer 4

You are solving this equation for x, so the goal is to end up with x alone on the left side of the equal sign and a plain number on the right side.

Answer 5

The first thing we need to do is to get rid of the fraction 2/3 from the left side.
Since 2/3 is multiplying a quantity in parentheses, we need to divide both sides by 2/3.
Dividing by 2/3 is the same as multiplying by 3/2, so we multiply both sides by 3/2.

Answer 6

okk...

Answer 7

\(\dfrac{2}{3}(x - 2) = 4x\)

\(\dfrac{3}{2} \times \dfrac{2}{3}(x - 2) = \dfrac{3}{2} \times 4x \)

Answer 8

x-2=6x?

Answer 9

On the left side, 3/2 and 2/3 cancel each other, which is what we wanted.
On the right side, we need to multiply 3/2 by 4x. 4x is the same as 4x/1

Answer 10

\(\dfrac{\cancel{3}}{\cancel{2}} \times \dfrac{\cancel{2}}{\cancel{3}}(x - 2) = \dfrac{3}{\cancel{2}~1} \times \cancel{4} ~2x \)

\(x - 2 = 6x\)

You are correct.

Answer 11

+2 to both sides?

Answer 12

Yes.

Answer 13

8x=x?

Answer 14

\(x - 2 = 6x\)

\(x = 6x + 2\)

Now we subtract 6x from both sides.

Answer 15

You need to be careful when adding terms.
Only like terms can be combined together.
Terms are like terms when the variable parts are the same.
5x and 2x are like terms. They add: 5x + 2x = 7x
6 and 2x are not like terms. They cannot combine together: 6 + 2x = 2x + 6 That's all you can do.

Answer 16

Ok, now we are up to this:

\(x = 6x + 2\)

We want all x's on the left side, so we subtract 6x from both sides.

\(x - 6x = 6x + 2 - 6x\)

\(-5x = 2\)

Ok so far?

Answer 17

yes..

Answer 18

Now we do the last step.
x is being multiplied by -5. To get rid of the multiplication by -5, we divide both sides by -5, since dividing is the opposite operation of multiplying.

\(\dfrac{-5x}{-5} = \dfrac{2}{-5} \)

Now we simplify both sides to get our final answer:

\(x = -\dfrac{2}{5} \)

Answer 19

Did you follow that?

Answer 20

yes.. so A?

Answer 21

Yes, the answer is choice A.

Answer 22

thanks!

Answer 23

You're welcome.