Let's evaluate each statement:
1. When x=2, both expressions have a value of 18.
- To check this, let's substitute x=2 into both expressions:
- \(7x+4 = 7(2) + 4 = 18\)
- \(3x+5+4x-1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 8 - 1 = 18\)
- This statement is true.
2. The expressions are only equivalent for x=4 and x-6.
- This statement is not entirely accurate because we've already shown they are equivalent for x=2 as well.
3. The expressions are only equivalent when evaluated with even values.
- This statement is not true because we've shown they are equivalent for x=2, which is an odd value.
4. The expressions have equivalent values for any value of x.
- This statement is not true since we've shown they are not equivalent for all values of x.
5. The expressions should have been evaluated with one odd value and one even value.
- This statement is partially true. We've evaluated the expressions for x=2, which is an even value, but we haven't tested with an odd value.
6. When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
- Let's check:
- \(7x+4 = 7(0) + 4 = 4\)
- \(3x+5+4x-1 = 3(0) + 5 + 4(0) - 1 = 5 - 1 = 4\)
- This statement is true.
7. The expressions have equivalent values if [missing continuation].
- This statement is incomplete, so it's unclear whether it's true or false.
Based on the given options, the true statements are:
- When x=2, both expressions have a value of 18.
- When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
