Final answer:
Like terms with 5x from the provided list are 4x, -8x, and -5x, because they all have the variable x raised to the same power. Terms with different powers or no variables, like 5x², 9x², and the constant 3, are not like terms with 5x.
Step-by-step explanation:
From the list provided, the terms that are like 5x are terms that can also be represented as a multiple of x with no other variables or exponents involved, except for the first power of x. In math, 'like terms' are terms that have the same variables raised to the same power. The terms that are like 5x from the given list are 4x, -8x, and -5x.
Examples:
- 4x is like 5x because they both have 'x' raised to the first power and only differ in their coefficients.
- -8x is also like 5x for the same reason, even though it has a negative coefficient.
- -5x is exactly like 5x but with an opposite sign.
Terms such as 5x², 9x², and constants like 3 are not like terms with 5x because they either have a different power of x or no variable x at all.