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Solve for xx.\newline(x−1)(x+6)≤0(x - 1)(x + 6) \leq 0\newline Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.

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Q. Solve for xx.\newline(x−1)(x+6)≤0(x - 1)(x + 6) \leq 0\newline Write 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 intervals.\newlineIntervals: (−∞,−6(-\infty, -6), (−6,1(-6, 1), (1,∞)(1, \infty).
  2. Test x=−7x = -7: Test x=−7x = -7 in (x−1)(x+6)(x - 1)(x + 6).\newline(−7−1)(−7+6)=(−8)(−1)=8(-7 - 1)(-7 + 6) = (-8)(-1) = 8, which is > 0.
  3. Test x=0x = 0: Test x=0x = 0 in (x−1)(x+6)(x - 1)(x + 6).(0−1)(0+6)=(−1)(6)=−6(0 - 1)(0 + 6) = (-1)(6) = -6, which is < 0.
  4. Test x=2x = 2: Test x=2x = 2 in (x−1)(x+6)(x - 1)(x + 6).(2−1)(2+6)=(1)(8)=8(2 - 1)(2 + 6) = (1)(8) = 8, which is > 0.
  5. Combine Intervals: Combine the intervals where the product is ≤0\leq 0. The solution is −6≤x≤1-6 \leq x \leq 1.

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