distributive property with fractions

Question

solve the problem

4x/5 - x = x/10 - 9/2

Answer 1

Multiplies everything by 10:

10( 4x/5) - 10x = 10(x/10) - 10(9/2)

8x - 10x = x - 45 <-- distributive

-2x = x - 45 <-- combines like terms

0 = 3x-45 <--- adds 2x to both sides

45 = 3x <-- adds 45 to both sides

x = 15 <-- divides by 3

check:

left side: 4*15/5 - 15 = 4*3-15 = 12-15 = -3

right side: 15/10 - 9/2 = 3/2 - 9/2 = -6/2 = -3

yes, it is correct...

x=15