Question

Please complete the following problems by combining like terms.

1) 5x - 6y + 8 + 7x + 6y

A) 12x + 2
B) 12x + 14
C) 12x + 8
D) 11x + 14

Answer 1

The correct answer is: 12x + 14, which represents the simplified expression after combining like terms in the given equation. Thus, the correct answer is option B.

Explanation:

Combining like terms involves grouping together similar terms. In the given expression, 5x and 7x are like terms as they both involve the variable 'x.' So, adding these gives us 12x. Similarly, -6y and +6y cancel each other out since they're opposites, resulting in zero. Then, combining the constant terms 8 and 0 gives us 14. Therefore, the final simplified expression is 12x + 14 (option B).

To solve this, first, combine the 'x' terms:

5x + 7x = 12x

Then, combine the 'y' terms:

-6y + 6y = 0

Combine the constant terms:

8 + 0 = 8

Therefore, the expression becomes:

12x + 8

But, don't forget to add the constant term (8) to the combined 'x' terms (12x):

12x + 8

Finally, simplify the constant term and you get:

12x + 14

Thus, the answer is 12x + 14, which is option B.

This process involved identifying like terms (terms with the same variables raised to the same power) and combining them accordingly. The constants were added separately after simplifying the variable terms. In this case, the variable terms resulted in 12x, and combining the constants gave us 14, resulting in the expression 12x + 14.

Answer 2

The simplified expression is 12x + 8 (Option C). To combine like terms, we merge the 'x' terms and 'y' terms separately. The 'y' terms cancel each other out and we are left with 12x for the variable terms, and the constant 8 remains the same, leading to the simplified expression 12x + 8.

Step-by-step explanation:

To solve the provided problem, we must combine like terms.

Like terms are terms that have the same variables raised to the same power.

In this case, we need to combine the terms with 'x' and the terms with 'y' separately, plus any constant numbers.

Combining the 'x' terms: 5x + 7x = 12x.

Combining the 'y' terms: -6y + 6y = 0 (they cancel each other out).

Adding the constant: 8 remains unchanged since there are no other constant terms to combine it with.

Therefore, the expression simplifies to: 12x + 8.

Hence, the correct answer is 12x + 8 (Option C).