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

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The equation is $\"\"$ .

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Write two cases:

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Case-1: a = b.

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$\"\"$

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Case-2: a = -b

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

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Solve the equation for Case-1.

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$\"\"$

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According to addition property of equality: if a = b, then a + c = b + c.

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$\"\"$ (Add 25 to each side)

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

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$\"\"$ (Add: 17 + 25 = 42)

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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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|17| = 17 (Subtract: $\"\"$ )

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The absolute value of 17 is 17.

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17 = 17

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Compare the values the equation is true. $\"\"$ is a solution. $\"\"$

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Solve the equation for Case-2.

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$\"\"$

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According to addition property of equality: if a = b, then a + c = b + c.

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$\"\"$ (Add 25 to each side)

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

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

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

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

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Compare the values the equation is true. $\"\"$ is a solution. $\"\"$

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The solutions are 42 and 8. The solution set is $\"\"$ .