Alright! Let's tackle the question step-by-step.
### Using the Distributive Property to Evaluate [tex]\( 4(2x - 1) \)[/tex] when [tex]\( x = 5 \)[/tex]:
1. Substitute [tex]\( x = 5 \)[/tex] into the expression:
[tex]\[
4 (2 \cdot 5 - 1)
\][/tex]
2. Simplify inside the parentheses first:
[tex]\[
2 \cdot 5 = 10
\][/tex]
So the expression inside the parentheses becomes:
[tex]\[
10 - 1
\][/tex]
3. Subtract to simplify further:
[tex]\[
10 - 1 = 9
\][/tex]
4. Apply the distributive property by multiplying:
[tex]\[
4 \cdot 9 = 36
\][/tex]
So, the result is [tex]\( 36 \)[/tex].
Among the given options, the correct answer is:
[tex]\[
36
\][/tex]
### Using the Commutative Property of Addition:
The commutative property of addition states that changing the order of addends does not change the sum. We need to apply this property to rewrite the given equation involving fractions.
The given equation is:
[tex]\[
\frac{13}{20} - \frac{2}{5} = \frac{1}{4}
\][/tex]
The commutative property of addition does not apply directly to subtraction. However, you could think of it in terms of converting subtraction to addition of a negative, but that would be overcomplicating things since the commutative property is purely about addition.
Thus, it seems there might be confusion between adding like terms, simplifying fractions, or another misunderstanding regarding the properties. Given the equations provided, none seem to fit the communitive build directly without further context.
Hope this clears up how to tackle both parts of the question!
