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Solve for xx.\newline (x + 4)(x - 4) < 0 \newlineWrite a compound inequality like 1 < x < 3 or like x < 1 or x > 3.

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Q. Solve for xx.\newline(x+4)(x−4)<0 (x + 4)(x - 4) < 0 \newlineWrite a compound inequality like 1<x<31 < x < 3 or like x<1x < 1 or x>3x > 3.
  1. Plot Zeros and Test Intervals: Plot the zeros on a number line and test the intervals. The intervals are (−∞,−4)(-\infty, -4), (−4,4)(-4, 4), and (4,∞)(4, \infty).
  2. Test Interval (−∞,−4): (-\infty, -4): Test the interval (−∞,−4) (-\infty, -4) by picking a number less than −4 -4 , say −5 -5 .(−5+4)(−5−4)=(−1)(−9)=9 (-5 + 4)(-5 - 4) = (-1)(-9) = 9 , which is \ (> 00 \).
  3. Test Interval (−4,4) (-4, 4) : Test the interval (−4,4) (-4, 4) by picking a number between −4 -4 and 4 4 , say 0 0 .(0+4)(0−4)=(4)(−4)=−16(0 + 4)(0 - 4) = (4)(-4) = -16, which is < 0.
  4. Test Interval (4,∞):(4, \infty): Test the interval (4,∞)(4, \infty) by picking a number greater than 44, say 55.(5+4)(5−4)=(9)(1)=9(5 + 4)(5 - 4) = (9)(1) = 9, which is > 0.
  5. Identify Solution Interval: Since we want (x + 4)(x - 4) < 0, the solution is the interval where the product is negative.\newlineThe product is negative in the interval (−4,4)(-4, 4).
  6. Write Compound Inequality: Write the solution as a compound inequality. -4 < x < 4.

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