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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

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  1. anonymous
    • one year ago
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    I am horrible at fractions, so any help would be great..

  2. mathstudent55
    • one year ago
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    Do you mean: \(\dfrac{2}{3}(x - 2) = 4x\)

  3. anonymous
    • one year ago
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    yes ma'am/ sir

  4. mathstudent55
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    okk...

  7. mathstudent55
    • one year ago
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    \(\dfrac{2}{3}(x - 2) = 4x\) \(\dfrac{3}{2} \times \dfrac{2}{3}(x - 2) = \dfrac{3}{2} \times 4x \)

  8. anonymous
    • one year ago
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    x-2=6x?

  9. mathstudent55
    • one year ago
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    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
    • one year ago
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    \(\dfrac{\cancel{3}}{\cancel{2}} \times \dfrac{\cancel{2}}{\cancel{3}}(x - 2) = \dfrac{3}{\cancel{2}~1} \times \cancel{4} ~2x \) \(x - 2 = 6x\) You are correct.

  11. anonymous
    • one year ago
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    +2 to both sides?

  12. mathstudent55
    • one year ago
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    Yes.

  13. anonymous
    • one year ago
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    8x=x?

  14. mathstudent55
    • one year ago
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    \(x - 2 = 6x\) \(x = 6x + 2\) Now we subtract 6x from both sides.

  15. mathstudent55
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    yes..

  18. mathstudent55
    • one year ago
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    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
    • one year ago
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    Did you follow that?

  20. anonymous
    • one year ago
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    yes.. so A?

  21. mathstudent55
    • one year ago
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    Yes, the answer is choice A.

  22. anonymous
    • one year ago
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    thanks!

  23. mathstudent55
    • one year ago
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    You're welcome.

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