x/5-2=x/2+3 solve for x

Solve for x:x/5 - 2 = x/2 + 3

Put each term in x/5 - 2 over the common denominator 5: x/5 - 2 = x/5 - (10) / 5:x/5 - (10) / 5 = x/2 + 3

x/5 - (10) / 5 = (x - 10) / 5: (x - 10) / 5 = x/2 + 3

Put each term in x/2 + 3 over the common denominator 2: x/2 + 3 = x/2 + 6/2: (x - 10) / 5 = x/2 + 6/2

x/2 + 6/2 = (x + 6) / 2: (x - 10) / 5 = (x + 6) / 2

Multiply both sides by 10: (10 (x - 10)) / 5 = (10 (x + 6)) / 2

10/5 = (5*2) / 5 = 2:2 (x - 10) = (10 (x + 6)) / 2

10/2 = (2*5) / 2 = 5:2 (x - 10) = 5 (x + 6)

Expand out terms of the left hand side:2 x - 20 = 5 (x + 6)

Expand out terms of the right hand side:2 x - 20 = 5 x + 30

Subtract 5 x from both sides: (2 x - 5 x) - 20 = (5 x - 5 x) + 30

2 x - 5 x = - 3 x:-3 x - 20 = (5 x - 5 x) + 30

5 x - 5 x = 0:-3 x - 20 = 30

Add 20 to both sides: (20 - 20) - 3 x = 20 + 30

20 - 20 = 0:-3 x = 30 + 20

30 + 20 = 50:-3 x = 50

Divide both sides of - 3 x = 50 by - 3: (-3 x) / (-3) = 50 / (-3)

(-3) / (-3) = 1:x = 50 / (-3)

Multiply numerator and denominator of 50 / (-3) by - 1:Answer: x = (-50) / 3