manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. her work is shown below.\n3 - 2|0.5x +…

manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. her work is shown below.\n3 - 2|0.5x + 1.5| = 2\n-2|0.5x + 1.5| = -1\n|0.5x + 1.5| = 0.5\n0.5x + 1.5 = 0.5\n0.5x = -1\nx = -2\nwhat is the other solution to the equation?\no x = -6\no x = -4\no x = 2\no x = 4

manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. her work is shown below.\n3 - 2|0.5x + 1.5| = 2\n-2|0.5x + 1.5| = -1\n|0.5x + 1.5| = 0.5\n0.5x + 1.5 = 0.5\n0.5x = -1\nx = -2\nwhat is the other solution to the equation?\no x = -6\no x = -4\no x = 2\no x = 4

Answer

Explanation:

Step1: Isolate the absolute - value expression

Starting from the equation (3 - 2|0.5x + 1.5|=2). First, subtract 3 from both sides: (-2|0.5x + 1.5|=2 - 3=-1). Then divide both sides by - 2, we get (|0.5x + 1.5| = 0.5).

Step2: Consider the two cases of the absolute - value equation

The absolute - value equation (|a|=b) ((b\geq0)) has two cases: (a = b) and (a=-b). We already know one case (0.5x+1.5 = 0.5) which gives (x=-2). For the second case, set (0.5x + 1.5=-0.5). Subtract 1.5 from both sides: (0.5x=-0.5 - 1.5=-2). Then divide both sides by 0.5: (x=\frac{-2}{0.5}=-4).

Answer:

(x = - 4)