I need to simplify this expression

This is Algebra I so I know you mean 1/2x as the fraction 1/2 times the variable x.

There are two sets of parenthesis where you need to distribute the outside factor. That means multiply each term inside the parenthesis by the outside factor.

1st work the left set of parenthesis

-10(1/2x - 1/5y) In this section notice that the denominators 2 and 5 work well with the number 10 because they are factors of 10.

Multiply Each Term by -10

-10(1/2x) = -5x and -10(1/5y) = -2y Why? Because half of -10 equals -5 and a fifth of -10 equals -2.

Rewrite the expression

The left parenthesis should now be simplified to -5x - (-2y) and further to

**-5x + 2y**because subtracting a negative is the same as adding a positive (integer subtraction rule).2nd work the right set of parenthesis.

30(1/6x + 4/5y) notice the denominators 6 and 5 work well with 30 because they are factors of 30.

Multiply each term by 30

30(1/6x) = 5x and 30(4/5y) = 24y

Why 24? Because 30(1/5) = 6 but they are asking for 4/5 which is 4*6

Rewrite the right side of the expression.

**5x + 24y**

**Now write them back together. -5x + 2y + 5x + 24y**

Combine the like terms

-5x + 5x = 0

and all that remains is

2y + 24y = 26y

**26y is the simplified expression**