We are tasked with solving the equation:

\[
-\frac{1}{2}(16x + 12) = 6 - 8x
\]

### Step 1: Distribute the \(-\frac{1}{2}\)
We will first distribute \(-\frac{1}{2}\) across the terms inside the parentheses:

\[
-\frac{1}{2} \times 16x = -8x
\]
\[
-\frac{1}{2} \times 12 = -6
\]

So the equation becomes:

\[
-8x - 6 = 6 - 8x
\]

### Step 2: Simplify the equation
Now, we'll add \(8x\) to both sides to eliminate the \(-8x\) on both sides:

\[
-6 = 6
\]

### Step 3: Analyze the result
After simplifying, we get \(-6 = 6\), which is a contradiction. This means that there is **no solution** to the equation. The original equation is inconsistent.

Would you like further clarification on any part of this process?

---

Here are five related questions you might find useful:
1. How can you identify if an equation has no solution?
2. What does it mean for an equation to have infinite solutions?
3. How can you solve equations with fractions?
4. What is the process for solving linear equations step by step?
5. How do you solve equations with variables on both sides?

**Tip**: Always check for contradictions or tautologies when simplifying equations, as they indicate no solution or infinite solutions, respectively.

This page provides a step-by-step solution to the linear equation -\frac{1}{2}(16x + 12) = 6 - 8x, demonstrating the use of the distributive property and analyzing contradictions that result in no solution. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation