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EXOEXOEXO

  • one year ago

((2x-3)/4)-((x-2)/3)=2

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  1. Jhannybean
    • one year ago
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    Thank you for using parenthesis respectively.

  2. EXOEXOEXO
    • one year ago
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    \[\frac{ 2x-3 }{ 4 }-\frac{ x-2 }{ 3 }=2\]

  3. Jhannybean
    • one year ago
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    Lets start by finding the LCM between \(4~,~ 3~,~ 1\) (since 2 is over 1)

  4. Jhannybean
    • one year ago
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    This will help turn our function into a linear problem and make it easier to solve

  5. EXOEXOEXO
    • one year ago
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    12?

  6. Jhannybean
    • one year ago
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    That's right, 12. Now we multiply all the terms by 12. \[(4)(3)\left[\frac{ 2x-3 }{ 4 }-\frac{ x-2 }{ 3 }=2\right]\]

  7. EXOEXOEXO
    • one year ago
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    when we multiply the whole equation by 12 do we multiply the numerator and the denominator too?

  8. Jhannybean
    • one year ago
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    YEs

  9. Jhannybean
    • one year ago
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    \[\frac{2x-3}{4} \cdot (4)(3)= 3(2x-3)\]\[-\frac{x-2}{3} \cdot (4)(3) = (4)(-x-2)\]\[2\cdot (4)(3) = 24\]

  10. Jhannybean
    • one year ago
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    Do you see what I mean?

  11. EXOEXOEXO
    • one year ago
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    I don't understand how you got 3(2x-3) and 4(-x-2)

  12. Jhannybean
    • one year ago
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    When I multiplied both the numerator and denominator by 12, or (4)(3), I see that the 4 in the denominator cancels with the 4 im multiplying by \[\frac{2x-3}{\cancel{4}} \cdot \cancel{(4)}(3)= 3(2x-3)\] Multiplying the second fraction by (4)(3), the 3 gets cancelled out the same way\[\frac{ x-2 }{ \cancel{3} } \cdot (4)\cancel{(3)} = 4(x-2)\]

  13. Jhannybean
    • one year ago
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    Sorry, forget about the negative infront of the second fraction for now, we'll deal with that later.

  14. Jhannybean
    • one year ago
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    Does that make more sense though?

  15. EXOEXOEXO
    • one year ago
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    yes

  16. Jhannybean
    • one year ago
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    Alright

  17. EXOEXOEXO
    • one year ago
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    I got x=12.5

  18. Jhannybean
    • one year ago
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    Alright let's see if that's correct

  19. Jhannybean
    • one year ago
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    \[3(2x-3)-4(x-2)=24\]\[6x-9-4x+8=24\]\[2x-1=24\]\[2x=25\]\[x=\frac{25}{2} =12.5 \qquad \checkmark\] Good job.

  20. EXOEXOEXO
    • one year ago
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    thank you!

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