Question

Use the expression below to answer parts (a) and (b):

5x - 3x - 4y + 1/3(6x - 12y).
a) Simplify the expression by combining like terms. (SHOW YOUR WORK.)

b) Express the answer from part (a) as an equivalent expression in factored form.

c) In the space below, PROVE how you know your expressions are equivalent to the original expression.

Answer 1

To simplify the expression 5x - 3x - 4y + 1/3(6x - 12y), we combine like terms to obtain 4x - 8y. For part (b), the factored form becomes 4(x - 2y). The equivalence of the expressions is shown through correct algebraic manipulations.

Step-by-step explanation:

To simplify the given expression 5x - 3x - 4y + 1/3(6x - 12y), start by combining like terms. First, distribute the 1/3 across the parentheses, which gives us:

5x - 3x - 4y + 2x - 4y,

which simplifies to:

(5x - 3x + 2x) - (4y + 4y)

(4x) - (8y)

Next, for part (b), express 4x - 8y in factored form:

4(x - 2y).

Finally, for part (c), to prove the expressions are equivalent:

Original expression: 5x - 3x - 4y + 1/3(6x - 12y)

Simplified expression: 4x - 8y

Factored form: 4(x - 2y)

Both simplified and factored forms are derived from the original by proper algebraic operations, ensuring their equivalence.