I don't know what to do.
Hosni fave the following argument that -(a+b)= -a+-b, for all intergers a and b. If the arqument is correct, suppy the missing reasons. If it is in correct explain why not.
-(a+b)=(-1)(a+b)
=(-1)a+(-1)b
=-a+-b
You have correctly shown that the distributive property distributes the negative.
If the argment is correct supply the missing reasons. what is the reason? I don't know.
The distributive property distributes the negative to both a and b.
To determine whether Hosni's argument that -(a+b) = -a+-b, for all integers a and b is correct, we can use basic properties of arithmetic.
First, let's analyze each step of the argument:
Step 1: -(a+b) = (-1)(a+b)
Explanation: The negative sign in front of (a+b) can be rewritten as (-1)(a+b) because multiplying by -1 is equivalent to negating the value.
Step 2: (-1)(a+b) = (-1)a + (-1)b
Explanation: When we distribute the (-1) to both terms inside the parentheses, we obtain (-1)a + (-1)b.
Step 3: (-1)a + (-1)b = -a + -b
Explanation: By applying the distributive property, we can conclude that (-1)a is equivalent to -a and (-1)b is equivalent to -b.
By analyzing the steps, we can see that the argument is indeed correct. Each step follows the properties of arithmetic, specifically the distributive property, which allows us to break up the multiplication.
Therefore, we can conclude that -(a+b) = -a + -b, for all integers a and b.