Final answer:
Equivalent expressions to -18 + 6n include 6(n - 3), 6n - 6 - 12, -2(9 - 3n), and 12 + 6n - 30, all obtained by using properties like the distributive property and combining like terms in different configurations.
Step-by-step explanation:
To create expressions that are equivalent to -18 + 6n, one could apply the distributive property or combine like terms in different ways. Here are four different equivalent expressions:
- 6(n - 3) — This is obtained by factoring out the greatest common factor, which is 6.
- 6n - 6 – 12 — By splitting the -18 into two parts, we highlight the relationship between the coefficients.
- -2(9 - 3n) — Here, each term in the original expression has been multiplied by -2.
- 12 + 6n - 30 — This expression is reached by adding and then subtracting a number that cancels itself out, keeping the value of the expression unchanged.
To check the equivalence of these expressions, they should simplify to the original expression, which can be verified by applying arithmetic operations.