QuestionAugust 24, 2025

9.) (|x|+2 y)/(-|x|) Evaluate x=-4 y=2

9.) (|x|+2 y)/(-|x|) Evaluate x=-4 y=2
9.) (|x|+2 y)/(-|x|) Evaluate x=-4 y=2

Solution
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Answer

-2 Explanation 1. Substitute the values Replace ( x ) with ( ( \(-4\) ) ) and ( y ) with ( ( \(2\) ) ) in the expression. 2. Calculate absolute value Compute ( ( \(|x|\) ) ): ( ( \(|-4| = 4\) ) ). 3. Simplify numerator Substitute into the numerator: ( |x| + 2y = 4 + 2(2) = 8\) ). 4. Simplify denominator Substitute into the denominator: ( ( \(-|x| = -4\) ) ). 5. Evaluate the expression Divide the simplified numerator by the denominator: \(\frac{8}{-4} = -2\).

Explanation

1. Substitute the values<br /> Replace ( x ) with ( \(-4\) ) and ( y ) with ( \(2\) ) in the expression.<br />2. Calculate absolute value<br /> Compute ( \(|x|\) ): ( \(|-4| = 4\) ).<br />3. Simplify numerator<br /> Substitute into the numerator: ( |x| + 2y = 4 + 2(2) = 8\) ).<br />4. Simplify denominator<br /> Substitute into the denominator: ( \(-|x| = -4\) ).<br />5. Evaluate the expression<br /> Divide the simplified numerator by the denominator: \(\frac{8}{-4} = -2\).
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