$\"\"$ $\"\"$

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The equation is $\"\"$ .

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Write two cases:

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Case-1: $\"\"$

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$\"\"$

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Case-2: $\"\"$

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$\"\"$ $\"\"$

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Solve the equation for Case-1.

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$\"\"$

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Apply subtraction property of equality: Subtract 11 from each side.

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$\"\"$

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Apply additive identity property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ ) $\"\"$

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Check:

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To check the solution, substitute $\"\"$ in original equation.

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$\"\"$

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$\"\"$ (Add: $\"\"$ )

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$\"\"$ (The absolute value of 42 is 42)

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Compare the values the equation is true.

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$\"\"$

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Solve the equation for Case-2.

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$\"\"$

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Apply subtraction property of equality: Subtract 11 from each side.

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$\"\"$

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Apply additive identity property: $\"\"$ )

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$\"\"$ (Subtract: $\"\"$ )

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$\"\"$

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Check:

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To check the solution, substitute $\"\"$ in original equation.

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$\"\"$

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$\"\"$ (Add: $\"\"$ )

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$\"\"$ (The absolute value of $\"\"$ is 42)

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Compare the values the equation is true.

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$\"\"$

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The solution set is $\"\"$ .