the expression quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity

The given algebraic expression is:

\[
\left( -\frac{2}{3} \cdot x - 6 \right) - \left( -14 + \frac{1}{6} \cdot x \right)
\]

Let's simplify it step by step:

### Step 1: Distribute and simplify inside the parentheses
- For the first part: \( -\frac{2}{3} \cdot x - 6 \)
  - No further simplification is needed here.

- For the second part: \( -\left( -14 + \frac{1}{6} \cdot x \right) \)
  - Distribute the negative sign across the parentheses:
  \[
  -(-14) = 14 \quad \text{and} \quad -\left(\frac{1}{6} \cdot x\right) = -\frac{1}{6} \cdot x
  \]
  So, the second part becomes:
  \[
  14 - \frac{1}{6} \cdot x
  \]

### Step 2: Combine both parts
Now, the expression looks like this:
\[
-\frac{2}{3} \cdot x - 6 + 14 - \frac{1}{6} \cdot x
\]

### Step 3: Combine like terms
- Combine the constants: \( -6 + 14 = 8 \)
- Combine the terms with \( x \):
  \[
  -\frac{2}{3} \cdot x - \frac{1}{6} \cdot x
  \]
  To combine these, find a common denominator for \( \frac{2}{3} \) and \( \frac{1}{6} \), which is 6:
  \[
  -\frac{2}{3} = -\frac{4}{6}, \quad \text{so now we have:} \quad -\frac{4}{6} \cdot x - \frac{1}{6} \cdot x = -\frac{5}{6} \cdot x
  \]

### Final Expression
The simplified expression is:
\[
-\frac{5}{6} \cdot x + 8
\]

This is the simplified form of the given expression.

Do you have any questions or need more details? Here are some related questions to explore:

1. How do you simplify expressions with fractions and variables?
2. What is the method for distributing negative signs in algebraic expressions?
3. How do you combine terms with different denominators?
4. What are like terms in an algebraic expression?
5. Can you explain how to factor a simplified expression like this?

**Tip:** When simplifying algebraic expressions, always combine like terms and be mindful of distributing negative signs correctly.

Simplify the algebraic expression (-2/3)x - 6 - (-14 + 1/6x) step by step. This problem covers key algebraic concepts, including distributing negative signs and combining like terms, making it suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation