## anonymous one year ago 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

1. anonymous

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

2. mathstudent55

Do you mean: $$\dfrac{2}{3}(x - 2) = 4x$$

3. anonymous

yes ma'am/ sir

4. mathstudent55

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.

5. mathstudent55

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.

6. anonymous

okk...

7. mathstudent55

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

8. anonymous

x-2=6x?

9. mathstudent55

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

10. mathstudent55

$$\dfrac{\cancel{3}}{\cancel{2}} \times \dfrac{\cancel{2}}{\cancel{3}}(x - 2) = \dfrac{3}{\cancel{2}~1} \times \cancel{4} ~2x$$ $$x - 2 = 6x$$ You are correct.

11. anonymous

+2 to both sides?

12. mathstudent55

Yes.

13. anonymous

8x=x?

14. mathstudent55

$$x - 2 = 6x$$ $$x = 6x + 2$$ Now we subtract 6x from both sides.

15. mathstudent55

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.

16. mathstudent55

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?

17. anonymous

yes..

18. mathstudent55

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: $$x = -\dfrac{2}{5}$$

19. mathstudent55

20. anonymous

yes.. so A?

21. mathstudent55

Yes, the answer is choice A.

22. anonymous

thanks!

23. mathstudent55

You're welcome.