x/5 - x/2= 3 + 3x/10?

Question

solve

Answer 1

2x - 5x = 30 + 3x
- 3x = 30 + 3x
- 6x = 30
x = - 5

Answer 2

you need to find the least common denominator so that you can get each expression in a fraction form with the same denominator for each one.

denominators are 2, 5 and 10. fortunately the factors of 10 are 2 and 5, so 10 is the LCD.

multiply the first expression by 2/2, the second by 5/5 and the third by 10/10

(2/2)(x/5)-(5/5)(x/2)=3(10/10)+3x/10
2x/10-5x/10=30/10+3x/10
now all the denominators are the same so make one fraction on each side of the = sign
(2x-5x)/10=(30+3x)/10
if the denominators are the same, the fractions are equal only if the numerators are equal
2x-5x=30+3x
add -3x to both sides and simplify
2x-5x-3x=30+3x-3x
-6x=30
multiply both sides by (-1/6) (divide by -6)
(-1/6)(-6x)=30(-1/6) or
-6x/-6=30/-6
x=-5
check your work
-5/5-(-5/2)=3+3(-5)/10
-1+5/2=3-15/10
-2/2+5/2=30/10-15/10
3/2=15/10=3/2 check

try x=5
5/5-5/2=3+3(5)/10
1-5/2=3+15/10
2/2-5/2=30/10+15/10
-3/2=45/10
-3/2=9/2 doesn't check

Answer 3

collect like terms
x/5-x/2-3x/10=3
-6x/10=3
cross multiply
3*10=-6x
30=-6x
30/-6=x
x=-5
thanks

Answer 4

x=5

(2x-5x)^10=(30+3X)^10
20x-50x=300+30x
30x+50x-20x=300
60x=-300
x=-300/60
x=-5