Answer:
A: The value of both expressions when w=1 is 28.
D: The two expressions are not equivalent.
Explanation:
Given expressions are:
4(3w+4)
and
16w+12
For w=1
First Expression:
4(3w+4)
= 4[3(1)+4]
=4(3+4)
=4(7)
=28
Second expression:
16w+12
= 16(1)+12
=16+12
=28
For w=3
First Expression:
4(3w+4)
= 4[3(3)+4]
=4(9+4)
=4(13)
=52
Second expression:
16w+12
= 16(3)+12
=48+12
=60
Now looking at the statements:
A: The value of both expressions when w=1 is 28.
The statement is true because our calculated values of both expressions are 28 for w=1.
B: The two expressions are equivalent.
The two expressions are not equivalent because their values at w=3 are not same.
C: The value of both expressions when w=1 is 16.
The value of both expression when w=1 is 28 so this statement is not correct
D: The two expressions are not equivalent.
We can see by comparing the values that both expressions are not equivalent.
E: The value of both expressions when w=3 is 52.
F: The value of both expressions when w=3 is 60.
Both statements are false because both expressions have different values at w=3 ..