Answer:
8/9
Step-by-step explanation:
2/3 + 1 / ( 2 2/5) - 1/x = 1/3 - 1 / ( 2 2/3)
Changing to improper fractions
2 2/5 = ((5*2+2) / 5 = 12/5
2 2/3 = ( 3*2+2) /3 = 8/3
2/3 + 1 / ( 12/5) - 1/x = 1/3 - 1 / ( 8/3)
1 over and improper fraction flips the improper fraction 1 / ( a/b) = b/a
2/3 + 5/12 - 1/x = 1/3 -3/8
Subtract 2/3 from each side
5/12 -1/x = 1/3 -2/3 -3/8
5/12 -1/x = -1/3 -3/8
Subtract 5/12 from each side
-1/x = -1/3 -3/8-5/12
Multiply each side by 24 to get rid of the fractions
-24/x = -24/3 -3*24/8 -5*24/12
-24/x = -8 -9 -10
-24/x = -27
Multiply each side by x
-24 = -27x
Divide by -27
-24/-27 =x
8/9 =x
