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Diano4ka-milaya [45]
3 years ago
10

Help me please! I need help!

Mathematics
1 answer:
RSB [31]3 years ago
7 0

Answer:

52 and 65 those are the ages of principles between 50%

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  • x ∈ [−2; 1] ∪ 3.5

Step-by-step explanation:

<h3>Given</h3>

<u>Inequality</u>: (x-1)(x+2)(2x-7)≤0

<h3>Solution: </h3>

<u>If we solve the corresponding equation (x-1)(x+2)(2x-7)²= 0, we get roots </u>

  • x =  -2, 1, 3.5

<u>We need to consider the following 4 intervals: </u>

  • (−∞; −2), [−2; 1], (1; 3.5), (3.5; ∞)

<u>1st interval</u> (−∞; −2)

  • The expression (x-1)(x+2)(2x-7)² is positive as two of the multiples are negative and one is always positive (square number), and therefore  does not satisfy the inequality.

<u>2nd interval</u>  [−2; 1]

  • The expression is negative as only one of the multiples is negative, and therefore the interval (−1; 2) satisfies the inequality.

<u>3rd interval</u> (1; 3.5)

  • The expression is positive as all the multiples are positive. Therefore, the interval (1; 3.5) also does not satisfy the inequality.

<u>4th interval</u>

  • The expression is positive as above, and therefore also does not satisfy the inequality.  

<u>So, the answer to the inequality is: </u>

  • x ∈ [−2; 1] ∪ 3.5
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