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

The answer to (x-5)/2 =(x+2)/3 is x=19

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

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

x = 19

Solution steps

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Expand

(x - 5) \cdot 3 : 3 x - 15

Expand

2 (x + 2) : 2 x + 4

3 x - 15 = 2 x + 4

Move

15

to the right side

3 x = 2 x + 19

Move

2 x

to the left side

x = 19

\frac{x}{16} = \frac{5}{4}

\frac{x}{2} - \frac{3}{2} = \frac{3 x}{4} + \frac{1}{12}

- \frac{5}{8} a - 4 = 1

45 x + 5 = 275

y, x = 2 y - 9