What is the answer to (2(2x+3))/3 =(5(x-2))/2 ?

The answer to (2(2x+3))/3 =(5(x-2))/2 is x=6

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(2(2x+3))/3 =(5(x-2))/2

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

x = 6

Solution steps

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

2 (2 x + 3) \cdot 2 = 3 \cdot 5 (x - 2)

Simplify

4 (2 x + 3) = 15 (x - 2)

Expand

4 (2 x + 3) : 8 x + 12

Expand

15 (x - 2) : 15 x - 30

8 x + 12 = 15 x - 30

Move

12

to the right side

8 x = 15 x - 42

Move

15 x

to the left side

- 7 x = - 42

Divide both sides by

- 7

x = 6

- 1 + \frac{3 x}{2} = \frac{9}{7} + x

5 (4 - x) = 7 - 3 x

y, x - y = - 12

180 - 5 x + 180 - 6 x + 180 - 7 x = 360

x - 1 = x + 3

What is the answer to (2(2x+3))/3 =(5(x-2))/2 ?
The answer to (2(2x+3))/3 =(5(x-2))/2 is x=6
Solve for x: (2(2x+3))/3 =(5(x-2))/2
The solution is x=6