Question - Solving Absolute Value Equations
mathmathematics problem solvingsquare root methodsolving absolute value equationsabsolute value property
Solution:
The equation provided in the image is |2x - 3|^2 = 16. To solve for x, we need to take the square root of both sides of the equation and then solve the resulting absolute value equation.Starting with the equation:|2x - 3|^2 = 16Take the square root of both sides to eliminate the square on the left side:|2x - 3| = √16Since the square root of 16 is 4, we have:|2x - 3| = 4The absolute value equation |2x - 3| = 4 can split into two possible equations because the absolute value of a number can be both positive and negative:2x - 3 = 4 or 2x - 3 = -4 For the first equation:2x - 3 = 42x = 7x = 7/2x = 3.5For the second equation:2x - 3 = -42x = -1x = -1/2x = -0.5Therefore, there are two possible values for x: 3.5 and -0.5.
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