Solve the equation x+2 1/3+1 1/4=5 1/2−1 5/8 using inverse operations.

Answer 1

First, we need to simplify both sides of the equation:

x + (2+1/3) + (1+1/4) = (5+1/2) - (1+5/8)

x + (7/3) + (5/4) = (11/2) - (13/8)

To add the mixed numbers on both sides, we need to convert them to improper fractions:

x + (21/3) + (5/4) = (44/8) - (13/8)

x + (7) + (5/4) = (31/8)

Now we can combine the whole numbers and fractions on the left side of the equation:

x + (28/4) + (5/4) = (31/8)

x + (33/4) = (31/8)

Next, we need to isolate the variable x by subtracting (33/4) from both sides:

x = (31/8) - (33/4)

To subtract fractions, we need a common denominator:

x = (31/8) - (66/8)

x = -35/8

Therefore, the solution to the equation is x = -35/8.