Question

Решить неравенство: 1. (х-9)(х-2)>0 2. (х-4)(х-5)<0

Answer 1

Скорее всего, вот так

Answer 2

To solve the inequalities, we'll use a common method known as the sign chart. First, we'll find the critical points by setting each factor equal to zero and then analyze the sign of the expression in different intervals to determine the regions where the inequality holds true.

1. (x - 9)(x - 2) > 0:

Step 1: Find the critical points by setting each factor equal to zero and solving for x.

x - 9 = 0 -> x = 9 x - 2 = 0 -> x = 2

Step 2: Create a sign chart using the critical points.

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|   x < 2   |   2 < x < 9   |   x > 9   |

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(x - 9)(x - 2) | + | - | + |

Step 3: Determine the sign of the expression in each interval.

• For x < 2: Both factors are negative, and the product is positive.
• For 2 < x < 9: One factor is negative (x - 9), and the other is positive (x - 2), so the product is negative.
• For x > 9: Both factors are positive, and the product is positive.

Step 4: Write down the solution to the inequality.

The inequality (x - 9)(x - 2) > 0 is satisfied in the intervals (-∞, 2) and (9, ∞).

2. (x - 4)(x - 5) < 0:

Step 1: Find the critical points by setting each factor equal to zero and solving for x.

x - 4 = 0 -> x = 4 x - 5 = 0 -> x = 5

Step 2: Create a sign chart using the critical points.

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|   x < 4   |   4 < x < 5   |   x > 5   |

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(x - 4)(x - 5) | - | + | - |

Step 3: Determine the sign of the expression in each interval.

• For x < 4: Both factors are negative, and the product is positive.
• For 4 < x < 5: One factor is negative (x - 4), and the other is positive (x - 5), so the product is negative.
• For x > 5: Both factors are negative, and the product is positive.

Step 4: Write down the solution to the inequality.

The inequality (x - 4)(x - 5) < 0 is satisfied in the interval (4, 5).

So, to summarize:

1. The solution to (x - 9)(x - 2) > 0 is: x < 2 or x > 9.
2. The solution to (x - 4)(x - 5) < 0 is: 4 < x < 5.