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Solve the absolute value equation the absolute value of (2x + 1), plus 3, equal to 12.
Ax = 4 and x = -5
Bx = 4 and x = -4
Cx = 6 and x = -5
Dx = 4.5 and x = -4.5
Answer & Solution
Correct answer: A. x = 4 and x = -5
1. Isolate the absolute value first by subtracting 3 from both sides.
2. That leaves the absolute value of 2x plus 1 equal to 9.
3. A quantity whose distance from zero is 9 is either 9 or negative 9, so write two equations.
4. The first is 2x plus 1 equal to 9, which gives 2x equal to 8 and x equal to 4.
5. The second is 2x plus 1 equal to negative 9, which gives 2x equal to negative 10 and x equal to negative 5.
6. So the two solutions are 4 and negative 5.
7. The pair 4 and negative 4 assumes the solutions must be opposites, which only happens when the inside is just 2x.
8. The pair 6 and negative 5 forgets to subtract the 3 before splitting the equation.
9. The pair 4.5 and negative 4.5 divides 9 by 2 without dealing with the added 1.
_Source: OpenStax College Algebra (CC BY 4.0), section 2.6 Other Types of Equations_