https://file.aiquickdraw.com/mathbot/file/1729278312129hk710w01.jpg

We are given the equation:

\[
3(4 - 2x) = -x + 1
\]

Let's solve it step by step.

### Step 1: Distribute the 3 on the left-hand side
\[
3(4 - 2x) = 3 \times 4 - 3 \times 2x = 12 - 6x
\]
Now the equation is:
\[
12 - 6x = -x + 1
\]

### Step 2: Move all terms involving \(x\) to one side
Add \(6x\) to both sides:
\[
12 = 6x - x + 1
\]
Simplify the right-hand side:
\[
12 = 5x + 1
\]

### Step 3: Move constant terms to the other side
Subtract 1 from both sides:
\[
12 - 1 = 5x
\]
\[
11 = 5x
\]

### Step 4: Solve for \(x\)
Divide both sides by 5:
\[
x = \frac{11}{5}
\]

Thus, the solution is:
\[
x = \frac{11}{5}
\]

### Answer:
The correct choice is **A**.

---

Would you like further details on any of the steps or explanations? Here are some related questions you could explore:

1. How do you verify solutions to linear equations?
2. What are the common properties of linear equations?
3. How does distribution work in algebraic expressions?
4. How can you solve equations with fractions?
5. What is the geometric interpretation of linear equations?

**Tip:** Always check your solution by plugging it back into the original equation to ensure correctness.

Learn how to solve the linear equation 3(4 - 2x) = -x + 1 with a step-by-step breakdown. This algebraic problem covers the distributive property and properties of equality, 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