https://file.aiquickdraw.com/mathbot/file/1728879753121hae2pg2j.jpg

The equation in the image appears to be:

\[
\frac{2x - 1}{-2} + \frac{4}{4} = 4x + 10
\]

Let me now solve this step by step:

### Step 1: Simplify the fractions
\[
\frac{2x - 1}{-2} = -\frac{2x - 1}{2}
\quad \text{and} \quad \frac{4}{4} = 1
\]

So the equation becomes:
\[
-\frac{2x - 1}{2} + 1 = 4x + 10
\]

### Step 2: Eliminate the fraction by multiplying through by 2
Multiply both sides of the equation by 2 to get rid of the denominator:
\[
2 \left(-\frac{2x - 1}{2} + 1\right) = 2(4x + 10)
\]

Simplifying both sides:
\[
-(2x - 1) + 2 = 8x + 20
\]

### Step 3: Expand and simplify
Distribute the negative sign on the left-hand side:
\[
-2x + 1 + 2 = 8x + 20
\]

Simplify:
\[
-2x + 3 = 8x + 20
\]

### Step 4: Solve for \(x\)
Move all terms involving \(x\) to one side and constant terms to the other side:
\[
-2x - 8x = 20 - 3
\]
\[
-10x = 17
\]

Now solve for \(x\):
\[
x = \frac{-17}{10} \quad \text{or} \quad x = -1.7
\]

### Final Answer:
\[
x = -1.7
\]

Would you like more details on any step or have any questions? 

Here are some related questions to expand your understanding:
1. What happens if you don't multiply both sides by 2 in Step 2?
2. Can you rewrite the problem differently without fractions from the start?
3. How would the solution change if the constant on the right side was different?
4. Why is it important to eliminate fractions when solving equations?
5. What happens if you make a small mistake while distributing terms?

**Tip:** Always double-check your signs when distributing, especially when working with negative numbers!

Solve the equation: \( \frac{2x - 1}{-2} + \frac{4}{4} = 4x + 10 \)

Step-by-step solution for solving a linear equation involving fractions: \( \frac{2x - 1}{-2} + \frac{4}{4} = 4x + 10 \). This guide covers simplifying fractions, using properties of equality, and distributing terms, suitable for students in Grades 8-10.

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