Lets solve the equation first: <span> 0.5 – |x – 12| = –0.25 </span>= 1/2 - |x - 12| = -1/4 = 2 - 4<span>|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: </span>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. <span>3.) A good first step for solving the equation is to split it into a positive case and a negative case. </span><span>5.) The negative case of this equation is x – 12 = –0.75.</span>