For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a val

[VJesus12]

For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Source: Veritas Prep

[swerve]

For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Source: Veritas Prep

Given \(a\%b = (a + b)(a - b)\) and \(5\% x = 9\), we have

\(5\% x = (5+x) \cdot (5-x) = 25 - x^2\)

So, \(25 -x^2 = 9 \Longrightarrow x^2 = 16 \Longrightarrow x = \pm 4\)

Therefore, the correct answer is A

[Scott@TargetTestPrep]

For all integers \(a\) and \(b,\) \(a\%b = (a + b)(a - b).\) If \(5\%x = 9,\) then which of the following could be a value of \(x?\)

A. -4
B. -3
C. 2
D. 3
E. 6

Answer: A

Solution:

Translating 5%x = 9 into a regular equation, we have:

(5 + x)(5 - x) = 9

25 - x^2 = 9

16 = x^2

x = 4 or -4

Answer: A