which statements are true for solving the equation 0.5 - |x - 12| = -0.25? check all that apply.\nthe…

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

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

Answer

Explanation:

Step1: Isolate the absolute - value term

First, subtract 0.5 from both sides of the equation (0.5−|x - 12|=-0.25). We get (-|x - 12|=-0.25 - 0.5=-0.75), then (|x - 12| = 0.75).

Step2: Split into positive and negative cases

The general rule for (|a|=b) ((b\geq0)) is to split it into two cases: (a = b) and (a=-b). For (|x - 12| = 0.75), the positive case is (x - 12=0.75) and the negative case is (x - 12=-0.75).

Step3: Analyze the number of solutions

Since we have two cases (x - 12 = 0.75) (which gives (x=12 + 0.75=12.75)) and (x - 12=-0.75) (which gives (x=12-0.75 = 11.25)), the equation has 2 solutions.

Answer:

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 negative case of this equation is (x - 12=-0.75).