solve this by isolating the absolute value: -|2x+4| = 2|x-1|-10

To solve this equation by isolating the absolute value, we have:

\[
-|2x + 4| = 2|x - 1| - 10
\]

1. **Eliminate the negative sign**: Multiply both sides by \(-1\) to make the absolute value positive.
   \[
   |2x + 4| = -2|x - 1| + 10
   \]

2. **Rewrite the equation**:
   Now we have:
   \[
   |2x + 4| = 10 - 2|x - 1|
   \]

3. **Isolate \( |x - 1| \) term**: Move \(2|x - 1|\) to the left side.
   \[
   |2x + 4| + 2|x - 1| = 10
   \]

This is as simplified as we can make it without further conditions, as absolute values require solving for cases based on sign changes in the expressions inside the absolute values.

Would you like to continue with case-by-case analysis for further steps? 

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### Related Questions:

1. How do we interpret an absolute value in an equation?
2. What are steps for solving an equation with multiple absolute values?
3. How can we check solutions in an absolute value equation?
4. Why do absolute values split into cases when solving?
5. Can we solve absolute value inequalities similarly?

### Tip:
When solving equations with absolute values, split the equation into cases based on possible sign changes inside the absolute values.

Solve this by isolating the absolute value: -|2x+4| = 2|x-1|-10

This solution walks through solving the absolute value equation -|2x+4| = 2|x-1|-10 by isolating absolute terms and handling case-by-case analysis. Understand core concepts like absolute value properties and isolation techniques in algebra, suited for Grades 9-11.

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