Final answer:
Expressions b (5(2x - 3) - 3(2x - 1)), d (4(x - 5) + 8), e (5x - 9 - x - 3), and f (2(2x - 6)) are equivalent to 4x - 12. They simplify to the original expression when terms are properly eliminated and simplified.
Step-by-step explanation:
Let's find out which expressions are equivalent to the expression 4x - 12.
- a. 4x - 2 + 14: This simplifies to 4x + 12, which is not correct. Thus, it's not equivalent.
- b. 5(2x - 3) - 3(2x - 1): Simplifying, we get 10x - 15 - 6x + 3 = 4x - 12, so it's equivalent.
- c. 0 - (4x + 12): Simplifying, we get -4x - 12, which means it is not equivalent as it does not match the positive coefficient of x in 4x - 12.
- d. 4(x - 5) + 8: Expanding yields 4x - 20 + 8, which simplifies to 4x - 12, making it equivalent.
- e. 5x - 9 - x - 3: Simplifying we have 4x - 12, which matches the original expression, so it's equivalent.
- f. 2(2x - 6): When simplified, this yields 4x - 12, which is equivalent.
To check the equivalence, we eliminate terms and simplify the algebra. We apply the multiplication rules for signs correctly when simplifying each expression (like in options b, d, e, and f) to find out that the equivalent expressions are b, d, e, and f.