Answer:
A, D, and G
Step-by-step explanation:
Let's try each of the answer choices, one by one.
A) Plug x = 2 into each expression and see what we get.
7x + 4 = 7 * 2 + 4 = 14 + 4 = 18
3x + 5 + 4x - 1 = 3 * 2 + 5 + 4 * 2 - 1 = 6 + 5 + 8 - 1 = 18
Since they're both 18 when x = 2, A is true.
B) The statement says that the expressions are <em>only </em>equal for x = 4 and x = 8, but as we saw from A, they're also equal when x = 2, so B is wrong.
C) Let's try to find a counterexample for this by plugging in an odd number into each expression, like 1:
7x + 4 = 7 * 1 + 4 = 7 + 4 = 11
3x + 5 + 4x - 1 = 3 * 1 + 5 + 4 * 1 - 1 = 3 + 5 + 4 - 1 = 11
We see that these two expressions are equivalent when x = 1, which is an odd number, so this contradicts the statement that they're <em>only</em> equal when x is even. C is wrong.
D) Let's combine like terms for the expression 3x + 5 + 4x - 1:
3x + 4x + 5 - 1 = 7x + 4
Notice that this is the exact same expression as the first one, which is 7x + 4 so that means for any x, these two expressions will always be the same. D is thus true.
E) This is not true because it's possible that two expressions aren't equivalent but have the same value for a certain odd number and a certain even number. E is incorrect.
F) Obviously, if the two expressions are equivalent, they will give the same answer for any input of x, including when x = 0, so F is wrong.
G) Again, the two expressions will always be equal, including when x = 8, so this statement is true.
The answers are A, D, and G.
Hope this helps!
