Final answer:
Three expressions equivalent to 2x + 4x - 15 are 3(2x - 5), 12x/2 - (30/2), and (7x - 15) - x. All simplify to the original expression of 6x - 15 when combined like terms are added or distributed.
Step-by-step explanation:
To find three expressions equivalent to 2x + 4x - 15, we first simplify the given expression by combining like terms. Since 2x and 4x are both terms with the variable x, we can add them together according to the rule that when two positive numbers add, the answer has a positive sign.
Combining 2x and 4x gives us:
6x - 15
Now, here are three equivalent expressions:
3(2x - 5) - This is equivalent because when you distribute the 3, you get 3*2x which is 6x, and 3*(-5) which is -15, resulting in 6x - 15.
12x/2 - (30/2) - This is equivalent because when you simplify the fractions, 12x/2 becomes 6x and 30/2 becomes 15, which again results in 6x - 15.
(7x - 15) - x - This is equivalent because it's essentially adding an x and then taking it away, meaning 7x - x gives us back 6x, and the -15 remains unchanged. Therefore, the expression simplifies to 6x - 15.