https://file.aiquickdraw.com/mathbot/file/172617540243895g70hye.jpg

The problem from the image is:

Solve for \(x\) in the equation:

\[
-2(1 - 4x) = 3x + 8
\]

The possible answers are:

1. \( \frac{6}{11} \)
2. 2
3. \( \frac{-10}{7} \)
4. -2

Now, let's solve the equation step by step.

### Step 1: Expand the left-hand side.
\[
-2(1 - 4x) = -2 + 8x
\]

So the equation becomes:
\[
-2 + 8x = 3x + 8
\]

### Step 2: Move all the terms involving \(x\) to one side.
\[
8x - 3x = 8 + 2
\]

Simplifying gives:
\[
5x = 10
\]

### Step 3: Solve for \(x\).
\[
x = \frac{10}{5} = 2
\]

### Final Answer:
The solution to the equation is \( x = 2 \), which corresponds to option 2.

Would you like any further details or clarifications? Here are 5 related questions:

1. How do you solve similar linear equations with fractions?
2. What are the steps to check if your solution is correct?
3. Can you solve linear equations with more than one variable?
4. How do you handle equations with parentheses and negative signs?
5. What happens if there are no solutions or infinite solutions?

**Tip:** Always double-check by substituting your solution back into the original equation.

Learn how to solve the linear equation -2(1 - 4x) = 3x + 8 with a step-by-step solution. This problem covers key algebraic concepts such as expanding equations and solving for the variable x. Suitable for students in Grades 7-9.

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