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