10(2x+2)-x=2(8x-8) solve the following linear equations

Let's solve the linear equation:

\[
10(2x + 2) - x = 2(8x - 8)
\]

### Step 1: Distribute the terms inside the parentheses
- Distribute \(10\) to both \(2x\) and \(2\) on the left side:
  \[
  10 \times 2x + 10 \times 2 = 20x + 20
  \]
- Distribute \(2\) to both \(8x\) and \(-8\) on the right side:
  \[
  2 \times 8x - 2 \times 8 = 16x - 16
  \]

Now the equation looks like:
\[
20x + 20 - x = 16x - 16
\]

### Step 2: Combine like terms
- Combine \(20x\) and \(-x\) on the left side:
  \[
  20x - x + 20 = 16x - 16
  \]
  \[
  19x + 20 = 16x - 16
  \]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other side
- Subtract \(16x\) from both sides:
  \[
  19x - 16x + 20 = -16
  \]
  \[
  3x + 20 = -16
  \]
- Subtract 20 from both sides:
  \[
  3x = -16 - 20
  \]
  \[
  3x = -36
  \]

### Step 4: Solve for \(x\)
- Divide both sides by 3:
  \[
  x = \frac{-36}{3}
  \]
  \[
  x = -12
  \]

### Final Answer:
\[
x = -12
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you solve the equation \(2(3x + 4) = 5(x - 1)\)?
2. What are the steps to isolate \(x\) in the equation \(4x - 7 = 2x + 9\)?
3. How do you solve the equation \(7x + 3 = 2(2x - 1) + x\)?
4. What happens if you have variables on both sides of the equation \(5x + 6 = 3x - 8\)?
5. How do you handle equations with fractions, like \(\frac{2x}{3} + 4 = \frac{x}{2} - 1\)?

**Tip:** When solving linear equations, always aim to simplify both sides as much as possible before isolating the variable.

Learn how to solve the linear equation 10(2x + 2) - x = 2(8x - 8) step-by-step with detailed explanations. This problem covers fundamental algebraic concepts including distributing terms, combining like terms, and isolating variables. Suitable for Grades 7-9 students.

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