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How many solutions does the equation the absolute value of (3x + 4) equal to negative 9 have?
AIt has one solution
BIt has two solutions
CIt has no solution
DIt has three solutions
Answer & Solution
Correct answer: C. It has no solution
1. An absolute value measures a distance, so it can never come out negative.
2. The right side here is negative 9, which no distance can equal.
3. So the equation has no solution at all.
4. Had the right side been positive there would have been two solutions, and zero would have given one.
_Source: OpenStax College Algebra (CC BY 4.0), section 2.6 Other Types of Equations_