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Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.

1.) The equation will have no solutions.

2.) A good first step for solving the equation is to subtract 0.5 from both sides of the equation.

3.) A good first step for solving the equation is to split it into a positive case and a negative case.

4.) The positive case of this equation is 0.5 – |x – 12| = 0.25.

5.) The negative case of this equation is x – 12 = –0.75.

6.) The equation will have only 1 solution

Verified Answer :

lets solve the equation first:
 0.5 – |x – 12| = –0.25
= 1/2 - |x - 12| = -1/4
= 2 - 4|x - 12| = -1
= 4|x - 12| = 3
= |x - 12| = 0.75
positive case, x >= 12
x - 12 = 0.75
x = 12.75
negative case, x < 12
x - 12 = -0.75
x = 11.25
So those are the two solutions.
These apply:
1.) The equation will have no solutions.
2.) A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
3.) A good first step for solving the equation is to split it into a positive case and a negative case.
5.) The negative case of this equation is x – 12 = –0.75.

the real answer is (2) A good first step for solving the equation is to subtract 0.5 from both sides of the equation.

(5) The negative case of this equation is x – 12 = –0.75.

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