Let's solve the equation step by step:

$-2(x+5) + 9(x-5) = -7x + 7(x-4)$

Step 1: Distribute the terms

Distribute $-2$ and $9$ on the left-hand side: $-2x - 10 + 9x - 45$

Distribute $-7$ and $7$ on the right-hand side: $-7x + 7x - 28$

Now the equation simplifies to: $(-2x + 9x - 10 - 45) = (-7x + 7x - 28)$

Step 2: Simplify both sides

$7x - 55 = 0 - 28$

$7x - 55 = -28$

Step 3: Solve for $x$

Add 55 to both sides: $7x = 27$

Divide by 7: $x = \frac{27}{7}$

Final Answer:

$x = \frac{27}{7}$

Would you like me to verify the solution by substituting it back?

Related Questions:

1. How do you check if a solution is correct in an algebraic equation?
2. What are the properties of equality used in solving equations?
3. How do you solve equations with fractions?
4. What happens when an equation has no solution?
5. How do you solve equations with variables on both sides?

Tip:

Always distribute carefully and combine like terms properly to avoid errors in solving equations.