Let's solve the equation step by step.

Given equation:  
\[ 5x - 8(2 - x) = -5(x - 3) \]

### Step 1: Distribute the constants
Distribute \(-8\) on the left side and \(-5\) on the right side:

\[ 5x - 8 \times 2 + 8x = -5x + 15 \]

This simplifies to:

\[ 5x - 16 + 8x = -5x + 15 \]

### Step 2: Combine like terms
Combine the \(x\) terms on both sides:

\[ 13x - 16 = -5x + 15 \]

### Step 3: Add \(5x\) to both sides to get all \(x\) terms on one side:
\[ 13x + 5x - 16 = 15 \]

This simplifies to:

\[ 18x - 16 = 15 \]

### Step 4: Add 16 to both sides to isolate the \(x\) term:
\[ 18x = 31 \]

### Step 5: Divide by 18 to solve for \(x\):
\[ x = \frac{31}{18} \]

So, the solution is:

\[ x = \frac{31}{18} \]

Would you like more details on this solution, or do you have any questions?

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Here are 5 related questions for further practice:

1. Solve: \( 7x - 3(4 - x) = 2(5x - 7) \).
2. Solve for \(y\): \( 4y + 5(2 - y) = 3y - 6 \).
3. Simplify and solve: \( 6(2x - 3) = 4x + 8 - 2x \).
4. What is the solution to \( 3(5 - x) - 4x = 2x + 1 \)?
5. Solve: \( 9x - 7 = 2(x + 3) - 4x \).

**Tip:** Always remember to distribute the constants correctly and combine like terms when solving linear equations.

Learn how to solve the linear equation 5x - 8(2 - x) = -5(x - 3) step-by-step. This problem involves basic algebraic concepts such as linear equations, distributive property, and combining like terms. Suitable for Grades 7-9.

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