The distributive property states that the product of a number and a sum is equal to the sum of the products of the number and each of the addends. In other words,

a(b + c) = ab + ac

where a, b, and c are any numbers.

To simplify -3(x-10)+x using the distributive property, we can rewrite the expression as follows:

-3(x-10)+x = -3x + 30 + x

Now, we can apply the distributive property to the first two terms:

-3x + 30 + x = (-3)(x) + (-3)(-10) + x

= -3x + 30 + x

Finally, we can combine the like terms:

= -2x + 30

Therefore, the simplified expression is -2x + 30.

Here is a step-by-step explanation of how to simplify the expression using the distributive property:

1. The first step is to distribute the -3 to the terms inside the parentheses.
   • -3(x-10) = (-3)(x) + (-3)(-10)
   • This gives us -3x + 30
2. The next step is to combine the like terms.
   • -3x + 30 + x = -2x + 30

The simplified expression is -2x + 30.