The equation in the image is:

$1 + x - 8 - x = x + 11 - (-7x - 8)$

Let's solve this step-by-step.

1. Simplify both sides of the equation:

   • On the left side: $1 + x - 8 - x$
     • The $x$ terms cancel out, so we are left with: $1 - 8 = -7$
   • On the right side: $x + 11 - (-7x - 8)$
     • Distribute the minus sign over $-7x - 8$: $x + 11 + 7x + 8 = 8x + 19$

   So, the equation simplifies to: $-7 = 8x + 19$

2. Isolate $x$:

   • Subtract 19 from both sides: $-7 - 19 = 8x$ $-26 = 8x$

   • Divide by 8 to solve for $x$: $x = -\frac{26}{8} = -\frac{13}{4}$

The solution to the equation is: $x = -\frac{13}{4}$

Would you like further clarification or additional details?

Here are some related questions to explore further:

1. How do we simplify expressions with variables on both sides?
2. What are common mistakes to avoid when solving linear equations?
3. How can we check if our solution to a linear equation is correct?
4. What methods are useful for solving equations with fractions?
5. How does distributing a negative sign affect an expression?

Tip: Always double-check your work by substituting your solution back into the original equation to verify its accuracy.