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?\n○ x = -6\n○ x = -4\n○ x = 2\n○ 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?\n○ x = -6\n○ x = -4\n○ x = 2\n○ x = 4

Answer

Explanation:

Step1: Recall absolute - value property

For (|a| = b) ((b\geq0)), (a = b) or (a=-b). We already have (|0.5x + 1.5|=0.5) from the given work. We found the solution when (0.5x+1.5 = 0.5). Now consider the case (0.5x+1.5=-0.5).

Step2: Solve the new equation

Subtract 1.5 from both sides of (0.5x+1.5=-0.5). (0.5x=-0.5 - 1.5) (0.5x=-2)

Step3: Isolate x

Divide both sides by 0.5. (x=\frac{-2}{0.5}=-4)

Answer:

x = - 4