Find the value of x if 3/2√3x-2 =2 .?

Question

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

Please help me out.

Answer 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)

Answer 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

Answer 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

^^

Answer 4

(3(√3x-2))/2=2

3√3x-2=4

9(3x-2)=16

27x=34

x=34/27

Answer 5

34/27

Answer 6

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

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

(3x-2)=16/9

3x=34/9

x=34/27

Answer 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