Question:

Find the value of x if 3/2√3x-2 =2 .?

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Question in words : find the value of x if 3 divided by 2 root of 3x-2 is equal to 2.

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  1. Divide both sides by 3/2

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

    We can say 2 / (3/2) is the same as 2 * 2/3 (flip 3/2 and change sign)

    sqrt (3x - 2) = 2 * (2/3)

    Square both sides:

    3x - 2 = (2 * (2/3)) ^ 2

    3x = 1.777 + 2

    x = 3.777 / 3 = 1.26 (2dp)


  2. Question must be presented in a clear fashion.

    3 / [ 2 √(3x - 2) ] = 2

    Can be read in ONE WAY ONLY whereas a lack of brackets causes great confusion.

    3 = 4 √(3x - 2)

    3 / 4 = √(3x - 2)

    9 / 16 = 3x - 2

    3x = 41 / 16

    x = 41 / 48


  3. 3/2 root(3x-2) = 2

    root(3X-2) = 2x(2/3)

    root(3X-2) = 4/3

            3X-2 = (4/3)x(4/3)   ----------> quadrate

          3X - 2 = 16/9

    9x(3X - 2) = 16

       27X - 18 = 16

              27X = 34

                X = 34/27

    ^^



  4. (3(√3x-2))/2=2

    3√3x-2=4

    9(3x-2)=16

    27x=34

    x=34/27

  5. 34/27

  6. 3/2sqrt( 3x-2 )=2

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

    (3x-2)=16/9

    3x=34/9

    x=34/27

  7. Writing the equation as

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

    Multiply both sides by 2sqrt(3x-2)

    [3/(2sqrt(3x-2))]*2sqrt(3x-2) = 2 * 2sqrt(3x-2)

    3 = 4sqrt(3x-2)

    Divide both sides by 4

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

    Square both sides

    (3/4)*(3/4) = 9/16 = 3x - 2

    Add 2 =32/16 to both sides

    9/16 + 32/16 = 41/16 = 3x

    Divide both sides by 3

    41/48 = 3x/3 = x

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