AnswersOnline Algebra Function Number ASolving Absolute Value EquationsQuestion 74274
74274
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Solving Absolute Value Equations

Question 74274 • Online Algebra, Function, Number A

Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.The equation will have no solutions.A good first step for solving the equation is to subtract 0.5 from both sides of the equation.A good first step for solving the equation is to split it into a positive case and a negative case.The positive case of this equation is 0.5 – |x – 12| = 0.25.The negative case of this equation is x – 12 = –0.75.The equation will have only 1 solution

Answer
A
The equation will have no solutions.
B
A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
C
A good first step for solving the equation is to split it into a positive case and a negative case.
D
The positive case of this equation is 0.5 – |x – 12| = 0.25.
E
The negative case of this equation is x – 12 = –0.75.
F
The equation will have only 1 solution

Explanation

Subtract 0.5 from both sides: −|x − 12| = −0.75. Multiplying by −1 gives |x − 12| = 0.75, whose negative case is x − 12 = −0.75, so B and E are true. The positive case would be x − 12 = 0.75, and the equation has two solutions, not zero or one.

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