To solve the equation \( x + 11 = -17 \) for the value of \( x \), you need to isolate \( x \). You can do this by subtracting 11 from both sides of the equation.
Here's how it looks step by step:
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Start with the equation: \[ x + 11 = -17 \]
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To isolate \( x \), subtract 11 from both sides: \[ x + 11 - 11 = -17 - 11 \]
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Simplifying both sides gives: \[ x = -28 \]
So, the number that should be added to both sides to solve for \( x \) is -11 (which you are actually subtracting to isolate \( x \)).