communicate mathematical ideas does
-|-4|=|-(-4)|? justify your answer.
I need help how to do this. thanks
no
-|-4}
= -4
|-(-4)|
= |4|
= 4
To determine whether the equation |-|-4|| = |-(-4)| is true, we need to understand the concept of absolute value and how it operates. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value.
Now let's solve the equation step by step:
1. |-|-4||:
- Start by evaluating the inner absolute value of -4.
- |-4| = 4, since the absolute value of -4 is positive 4.
- Now we need to find the absolute value of 4.
- Since 4 is already positive, its absolute value is still 4.
- Hence, |-|-4|| = 4.
2. |-(-4)|:
- Start by evaluating -(-4). The negative sign in front of the parentheses means we need to change the sign of -4 to positive.
- -(-4) becomes +4.
- Now we need to find the absolute value of 4.
- Since 4 is positive, its absolute value remains 4.
- Hence, |-(-4)| = 4.
Since both |-|-4|| and |-(-4)| equal 4, we can conclude that |-|-4|| = |-(-4)|. The equation is justified.
The key to solving this problem was understanding how absolute value operates. By correctly applying the concept of absolute value and conducting the necessary calculations, we were able to determine that both sides of the equation are equal.