Question

12 what are the solutions to the equation $7(x + 13)(x - 7)=0$? a $x = \\{-6337, 0\\}$ b $x = \\{7, 0\\}$ c $x = \\{-13, 7\\}$ d $x = \\{-7, 13\\}$ e $x = \\{-13, -20\\}$ f $x = \\{-7, 7\\}$

Explanation:

Step1: Recall Zero - Product Property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). For the equation \(7(x + 13)(x - 7)=0\), we can consider the factors \(7\), \((x + 13)\) and \((x - 7)\). Since \(7
eq0\) (a non - zero constant), we set the other factors equal to zero.

Step2: Solve for \(x\) from each factor

• For the factor \((x + 13)\): Set \(x+13 = 0\). Subtract 13 from both sides of the equation: \(x=- 13\).
• For the factor \((x - 7)\): Set \(x - 7=0\). Add 7 to both sides of the equation: \(x = 7\).

Answer:

C. \(x=\{-13,7\}\)