Step 1: Simplify the equation
To solve the equation x/3 - 2x/5 = 2x/3 - 11/30, we need to simplify it by getting rid of any fractions. To do this, we can find a common denominator for all the fractions involved.

Step 2: Finding the common denominator
The common denominator for 3, 5, and 30 is 30. We need to multiply each term by a factor that will make the denominator equal to 30.

Step 3: Multiply each term by the appropriate factor
To make the denominator of the first term x/3 equal to 30, we need to multiply it by 10. So, we have (10 * x)/3.

To make the denominator of the second term 2x/5 equal to 30, we need to multiply it by 6. So, we have (6 * 2x)/5.

To make the denominator of the third term 2x/3 equal to 30, we need to multiply it by 10. So, we have (10 * 2x)/3.

To make the denominator of the fourth term 11/30 equal to 30, we need to multiply it by 30. So, we have 11.

Step 4: Simplify the equation further
After multiplying each term by the appropriate factor, our equation becomes:

(10 * x)/3 - (6 * 2x)/5 = (10 * 2x)/3 - 11

Simplifying each term further, we have:

(10x)/3 - (12x)/5 = (20x)/3 - 11

Step 5: Combine like terms
To combine like terms, we need to find a common denominator for the fractions involved. In this case, the common denominator is 15.

Multiplying each term by the appropriate factor, we have:

(50x)/15 - (36x)/15 = (100x)/15 - 11

Simplifying further, we get:

(14x)/15 = (100x)/15 - 11

Step 6: Isolate the variable term
To isolate the variable term, we need to move all other terms to the other side of the equation. In this case, we will move the (100x)/15 and -11 terms to the left side.

Subtracting (100x)/15 and -11 from both sides of the equation, we have:

(14x)/15 - (100x)/15 + 11 = 0

Step 7: Combine like terms
Combining the like terms on the left side of the equation, we have:

(14x - 100x + 165)/15 = 0

Simplifying further, we get:

(-86x + 165)/15 = 0

Step 8: Solve for x
To solve for x, we need to get rid of the denominator. Since the denominator is 15, we can multiply both sides of the equation by 15 to cancel it out.

Multiplying both sides by 15, we have:

15 * (-86x + 165)/15 = 0 * 15