Solve the equation x + 2 /13 = 5 2/3 using inverse operations.

Answer 1

To solve the equation x + 2/13 = 5 2/3, we need to isolate x on one side of the equation.

First, let's rewrite 5 2/3 as an improper fraction.

5 2/3 = (5 * 3 + 2)/3 = 17/3

Now, subtract 2/13 from both sides of the equation:

x + 2/13 - 2/13 = 17/3 - 2/13

Simplifying both sides:

x = 17/3 - 2/13

To add these fractions, we need to have a common denominator. The common denominator of 3 and 13 is 39.

x = (17/3)(13/13) - (2/13)(3/3) = 221/39 - 6/39

Now, we can combine the fractions:

x = (221 - 6)/39 = 215/39

Therefore, the solution to the equation x + 2/13 = 5 2/3 is x = 215/39.