Let's simplify the expression step by step:

The given expression is:
\[
12 \frac{5}{6}x - 14x + \frac{1}{6}x
\]

### Step 1: Convert the mixed number \(12 \frac{5}{6}\) to an improper fraction.
\[
12 \frac{5}{6} = \frac{72}{6} + \frac{5}{6} = \frac{77}{6}
\]
So the expression becomes:
\[
\frac{77}{6}x - 14x + \frac{1}{6}x
\]

### Step 2: Combine like terms.
The terms that have \(x\) in them are:
\[
\left(\frac{77}{6}x + \frac{1}{6}x\right) - 14x
\]

First, add \(\frac{77}{6}x\) and \(\frac{1}{6}x\):
\[
\frac{77}{6}x + \frac{1}{6}x = \frac{78}{6}x = 13x
\]

Now the expression is:
\[
13x - 14x
\]

### Step 3: Subtract the terms.
\[
13x - 14x = -x
\]

So the simplified expression is:
\[
-x
\]

### Final Answer:
The simplified expression is \(-x\).

Would you like further details or have any questions?

Here are 5 related questions you might be interested in:
1. How do you simplify more complex algebraic expressions?
2. What are some common mistakes when combining like terms?
3. How do you handle mixed numbers in algebraic expressions?
4. What is the importance of converting mixed numbers into improper fractions?
5. How do you simplify expressions with multiple variables?

**Tip:** Always double-check for like terms and ensure that coefficients and variables are treated consistently when simplifying expressions.

Learn how to simplify the algebraic expression 12 5/6x - 14x + 1/6x step-by-step. This problem covers key algebraic concepts, including converting mixed numbers to improper fractions and combining like terms. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation