Let’s go step by step for these exercises. I’ll solve a few problems for demonstration and explain the process so you can work on the rest.

Part C: Express each equation as another equivalent equation

1. $x - 6 = -3x + 10$

   Solution:

   • Add $3x$ to both sides: $x + 3x - 6 = 10$
   • Combine like terms: $4x - 6 = 10$
   • Add $6$ to both sides: $4x = 16$
   • Equivalent equation: $4x = 16$.

2. $2x + 7 = x - 6$

   Solution:

   • Subtract $x$ from both sides: $2x - x + 7 = -6$
   • Combine like terms: $x + 7 = -6$
   • Subtract $7$ from both sides: $x = -13$
   • Equivalent equation: $x = -13$.

Part D: Solve each equation

4. $11x - 7 = 5 - x$

   Solution:

   • Add $x$ to both sides: $11x + x - 7 = 5$
   • Combine like terms: $12x - 7 = 5$
   • Add $7$ to both sides: $12x = 12$
   • Divide by $12$: $x = 1$

5. $2 - 8x = 10x + 20$

   Solution:

   • Subtract $10x$ from both sides: $2 - 8x - 10x = 20$
   • Combine like terms: $2 - 18x = 20$
   • Subtract $2$ from both sides: $-18x = 18$
   • Divide by $-18$: $x = -1$

6. $17 - 3x = 2 + 2x$

   Solution:

   • Subtract $2x$ from both sides: $17 - 3x - 2x = 2$
   • Combine like terms: $17 - 5x = 2$
   • Subtract $17$ from both sides: $-5x = -15$
   • Divide by $-5$: $x = 3$

Do you want me to solve the remaining problems or go into more detailed explanations? Let me know!

Relative Questions:

1. What is the strategy for isolating variables in linear equations?
2. How do you justify the equivalence of equations after transformations?
3. Why is it important to check solutions for equations?
4. How do fractional coefficients in equations affect the solving process?
5. What are common mistakes to avoid when solving linear equations?

Tip: Always simplify each step to avoid errors when solving equations.