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

Answer 1

To solve the equation, we need to isolate the variable x.

Step 1: Convert the mixed number 5/2/3 to an improper fraction.
To do this, multiply the whole number (5) by the denominator of the fraction (3), then add the numerator (2) to get the new numerator. The denominator remains the same. Therefore, 5/2/3 is equivalent to (5 × 3 + 2)/3 = 17/3.

Step 2: Rewrite the equation with the improper fraction.
x + 2/3 = 17/3

Step 3: To remove the fraction, we multiply both sides of the equation by the reciprocal of the fraction's denominator.
3(x + 2/3) = 3(17/3)

Step 4: Simplify both sides of the equation.
3x + 2 = 17

Step 5: Isolate the variable by subtracting 2 from both sides.
3x + 2 - 2 = 17 - 2
3x = 15

Step 6: Finally, divide both sides of the equation by 3 to solve for x.
3x/3 = 15/3
x = 5

The solution to the equation x + 2/3 = 5/2/3 is x = 5.