What is the answer to this math problem

What is the answer to this math problem: 12 5/6x – 14x + 1/6x

The Correct Answer and Explanation is:

Final Answer:

The simplified result of the expression 12 5/6x – 14x + 1/6x is
–1/6x

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Step-by-Step Explanation:

We are given the algebraic expression:
12 5/6x – 14x + 1/6x

Step 1: Convert the mixed number to an improper fraction

12 5/6 is a mixed number. To simplify the expression, convert it to an improper fraction: 1256=12×6+56=77612 \frac{5}{6} = \frac{12 \times 6 + 5}{6} = \frac{77}{6}

So, the expression becomes: 776x−14x+16x\frac{77}{6}x – 14x + \frac{1}{6}x

Step 2: Combine like terms

All terms contain x, so we can factor x and combine the coefficients: (776−14+16)x\left(\frac{77}{6} – 14 + \frac{1}{6}\right)x

Now calculate the numerical part:

1. Combine the two fractions first:

776+16=786=13\frac{77}{6} + \frac{1}{6} = \frac{78}{6} = 13

2. Now subtract 14:

13−14=−113 – 14 = -1

So the entire expression simplifies to: (−1)x=−x(-1)x = -x

But let’s double-check with fractions for clarity: (776+16−14)x=(786−14)x=(13−14)x=−1x\left(\frac{77}{6} + \frac{1}{6} – 14\right)x = \left(\frac{78}{6} – 14\right)x = \left(13 – 14\right)x = -1x

Or, expressed as a fraction: −11x=−x\frac{-1}{1}x = -x

To express it using a fractional coefficient, we can write: −11x=−16x(Wait! This suggests an error. Let’s go back.)- \frac{1}{1}x = -\frac{1}{6}x \quad \text{(Wait! This suggests an error. Let’s go back.)}

Wait — let’s fix that. The error is in the assumption that: 13−14=−1613 – 14 = -\frac{1}{6}

That’s incorrect. 13 – 14 = -1, not -1/6.

BUT looking back: 776x−14x+16x=(77+16−14)x=(786−14)x=(13−14)x=−1x=−x\frac{77}{6}x – 14x + \frac{1}{6}x = \left(\frac{77 + 1}{6} – 14\right)x = \left(\frac{78}{6} – 14\right)x = (13 – 14)x = -1x = -x

So the correct answer is: −x\boxed{-x}

Why It’s Important to Be Careful:

This problem mixes fractions, whole numbers, and algebra. The key is aligning like terms and using a common denominator. Mixed numbers like 12 5/6 can trick you unless properly converted. After combining all like terms and simplifying carefully, we find that all the parts lead to just –x.

So, the correct and final simplified answer is:

✅ –x (or written as –1x)