Question

determine whether the following statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. the equation (2x - 3)^2 = 25 is equivalent to 2x - 3 = 5. choose the correct answer below. a. the statement is false. a true statement is \the equation (2x - 3)^2 = 25 is equivalent to 2x - 3 = - 5.\ b. the statement is true. c. the statement is false. a true statement is \the equation (2x - 3)^2 = 25 is equivalent to 2x - 3 = 25 or 2x - 3 = - 25.\ d. the statement is false. a true statement is \the equation (2x - 3)^2 = 25 is equivalent to 2x - 3 = 5 or 2x - 3 = - 5.\

Explanation:

Step1: Recall square - root property

If \(u^{2}=a\) (\(a\geq0\)), then \(u = \sqrt{a}\) or \(u=-\sqrt{a}\). Here \(u = 2x - 3\) and \(a = 25\).
Since \(\sqrt{25}=5\) and \(-\sqrt{25}=- 5\), if \((2x - 3)^{2}=25\), then \(2x - 3 = 5\) or \(2x - 3=-5\).

Answer:

D. The statement is false. A true statement is "The equation \((2x - 3)^{2}=25\) is equivalent to \(2x - 3 = 5\) or \(2x - 3=-5\)."