What is the answer to (2(x-1))/3 =(3(2x-1))/2 ?

The answer to (2(x-1))/3 =(3(2x-1))/2 is x= 5/14

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(2(x-1))/3 =(3(2x-1))/2

\frac{2 ( x - 1 )}{3} = \frac{3 ( 2 x - 1 )}{2}

x = \frac{5}{14}

Decimal Notation

x = 0.35714 \dots

Solution steps

\frac{2 ( x - 1 )}{3} = \frac{3 ( 2 x - 1 )}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

2 (x - 1) \cdot 2 = 3 \cdot 3 (2 x - 1)

Simplify

4 (x - 1) = 9 (2 x - 1)

Expand

4 (x - 1) : 4 x - 4

Expand

9 (2 x - 1) : 18 x - 9

4 x - 4 = 18 x - 9

Move

4

to the right side

4 x = 18 x - 5

Move

18 x

to the left side

- 14 x = - 5

Divide both sides by

- 14

x = \frac{5}{14}

- 1 + 4 a - 4 a^{2}

7 (\frac{x}{2} - (\frac{x}{3} - (\frac{x}{4} + 5))) = 140

2 x^{2} = 21 x - 49

x + 1 = 2 x + 8

\frac{1}{4} w = ∣ 4 w ∣

What is the answer to (2(x-1))/3 =(3(2x-1))/2 ?
The answer to (2(x-1))/3 =(3(2x-1))/2 is x= 5/14
Solve for x: (2(x-1))/3 =(3(2x-1))/2
The solution is x= 5/14