Let's evaluate both expressions at [tex]\( v = 3 \)[/tex] and [tex]\( v = 6 \)[/tex]:
Step 1: Evaluate the first expression [tex]\( 3v + 2(v + 1) - 4 \)[/tex] at [tex]\( v = 3 \)[/tex]:
[tex]\[ 3(3) + 2(3 + 1) - 4 \][/tex]
[tex]\[ = 9 + 2(4) - 4 \][/tex]
[tex]\[ = 9 + 8 - 4 \][/tex]
[tex]\[ = 13 \][/tex]
Step 2: Evaluate the second expression [tex]\( 16 + 3v - v \)[/tex] at [tex]\( v = 3 \)[/tex]:
[tex]\[ 16 + 3(3) - 3 \][/tex]
[tex]\[ = 16 + 9 - 3 \][/tex]
[tex]\[ = 22 \][/tex]
Step 3: Evaluate the first expression [tex]\( 3v + 2(v + 1) - 4 \)[/tex] at [tex]\( v = 6 \)[/tex]:
[tex]\[ 3(6) + 2(6 + 1) - 4 \][/tex]
[tex]\[ = 18 + 2(7) - 4 \][/tex]
[tex]\[ = 18 + 14 - 4 \][/tex]
[tex]\[ = 28 \][/tex]
Step 4: Evaluate the second expression [tex]\( 16 + 3v - v \)[/tex] at [tex]\( v = 6 \)[/tex]:
[tex]\[ 16 + 3(6) - 6 \][/tex]
[tex]\[ = 16 + 18 - 6 \][/tex]
[tex]\[ = 28 \][/tex]
Step 5: Determine if the expressions are equivalent.
To determine if the expressions are equivalent, their values must be the same for all values of [tex]\( v \)[/tex]. From our evaluations:
- When [tex]\( v = 3 \)[/tex]:
- The first expression gives [tex]\( 13 \)[/tex]
- The second expression gives [tex]\( 22 \)[/tex]
- When [tex]\( v = 6 \)[/tex]:
- Both expressions give [tex]\( 28 \)[/tex]
Since the values of the expressions are not the same for [tex]\( v = 3 \)[/tex], we can conclude that the expressions are not equivalent.
Based on the step-by-step evaluation above, the true statements are:
1. The value of both expressions when [tex]\( v = 6 \)[/tex] is 28.
2. The expressions are not equivalent.
So, the true statements are:
- The value of both expressions when [tex]\( v = 6 \)[/tex] is 28.
- The expressions are not equivalent.
