https://file.aiquickdraw.com/mathbot/file/1725553322242fxd59vrr.jpg

The equation extracted from the image is:

\[ 5x - (x - 18) = 6 - 2(x + 15) \]

Let's solve this step by step.

### Step 1: Distribute the negative signs
- On the left-hand side: \( 5x - (x - 18) = 5x - x + 18 \)
- On the right-hand side: \( 6 - 2(x + 15) = 6 - 2x - 30 \)

So, the equation becomes:
\[ 5x - x + 18 = 6 - 2x - 30 \]

### Step 2: Combine like terms
- Left-hand side: \( 5x - x = 4x \), so \( 4x + 18 \)
- Right-hand side: \( 6 - 30 = -24 \), so \( -2x - 24 \)

Now, the equation is:
\[ 4x + 18 = -2x - 24 \]

### Step 3: Move all \(x\) terms to one side and constants to the other
- Add \(2x\) to both sides: \( 4x + 2x + 18 = -24 \)
- Combine: \( 6x + 18 = -24 \)

### Step 4: Isolate \(x\)
- Subtract 18 from both sides: \( 6x = -24 - 18 \)
- Simplify: \( 6x = -42 \)
- Divide both sides by 6: \( x = \frac{-42}{6} = -7 \)

### Final Answer:
\[ x = -7 \]

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

Here are 5 related questions for practice:
1. What happens if you move the constants first instead of the \(x\) terms?
2. How would you verify the solution by substituting \(x = -7\) into the original equation?
3. What is the importance of distributing negative signs correctly in equations?
4. How would this process change if there were fractions involved?
5. What would happen if both sides of the equation contained the same expression?

**Tip**: Always double-check your distribution and combination of like terms to avoid common algebraic errors.

Solve the equation: 5x - (x - 18) = 6 - 2(x + 15)

Learn how to solve the linear equation 5x - (x - 18) = 6 - 2(x + 15) step-by-step, involving distribution and combining like terms. This problem is ideal for students in Grades 7-10.

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