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.)

Answer 1

The algebraic expression 5x-3x-4y+1/3(6x-12y) simplifies to 4x-8y by combining like terms and distributing the fraction. The final answer is reasonable upon review.

Step-by-step explanation:

To simplify the algebraic expression given as 5x-3x-4y+ 1/3 (6x-12y), we should first eliminate terms by combining like terms and then distribute the fraction within the parenthesis.

Here's the step-by-step simplification:

1. Combine the x terms: 5x - 3x = 2x.
2. Distribute the fraction 1/3 across the terms (6x-12y): 1/3 * 6x = 2x and 1/3 * (-12y) = -4y.
3. Now, combine the x terms and y terms: 2x + 2x and -4y - 4y.
4. Finally, the simplified expression is 4x - 8y.

After simplifying, we must check the answer to see if it is reasonable. The reduced terms indicate that no further simplification is possible, which seems reasonable.