Question

(х-1)(х-7)<0 полное решение

Answer 1

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Answer 2

To find the full solution to the inequality $(x-1)(x-7) < 0$, we need to determine the intervals where the inequality holds true. The inequality is already in factored form, so we can use a sign chart to analyze it.

1. Find the critical points by setting each factor to zero and solving for $x$: $(x - 1) = 0 \Rightarrow x = 1$ $(x - 7) = 0 \Rightarrow x = 7$

2. Create a sign chart with the critical points and test points from each interval: We'll choose test points $x = 0$, $x = 2$, and $x = 8$ (pick numbers less than 1, between 1 and 7, and greater than 7).

   Interval	$(x-1)$	$(x-7)$	$(x-1)(x-7)$
   $x < 1$	-	-	+
   $1 < x < 7$	+	-	-
   $x > 7$	+	+	+

3. Analyze the sign chart: The inequality $(x-1)(x-7) < 0$ holds true in the intervals where the product is negative (i.e., negative sign). These intervals are $1 < x < 7$.

Therefore, the full solution to the inequality $(x-1)(x-7) < 0$ is $1 < x < 7$.