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CLAT Exam  >  CLAT Questions  >  The inequality of p2 + 5 < 5p + 14 can be ... Start Learning for Free
The inequality of p2 + 5 < 5p + 14 can be satisfied if:
  • a)
    p ≥ 6, p = 1 
  • b)
    p = 6, p = −2
  • c)
    p ≤ 6, p ≤ 1
  • d)
    p ≤ 6, p > −1
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The inequality of p2 + 5 < 5p + 14 can be satisfied if:a)p ≥ 6, ...
We have, p2 + 5 < 5p + 14
=> p2 – 5p – 9 < 0

=> p<6.4 or p>-1.4
Hence, p ≤ 6, p > −1 will satisfy the inequalities
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Most Upvoted Answer
The inequality of p2 + 5 < 5p + 14 can be satisfied if:a)p ≥ 6, ...
Explanation:

Given Inequality: p^2 + 5 < 5p="" +="" />

Step 1: Rearrange the Inequality:
To simplify the inequality, we need to rearrange it so that all terms are on one side of the inequality sign:
p^2 - 5p - 9 < />

Step 2: Factorize the Quadratic Equation:
To solve the inequality, we first need to factorize the quadratic equation:
(p - 6)(p + 1) < />

Step 3: Find the Critical Points:
The critical points are where the inequality changes sign. In this case, the critical points are when p = 6 and when p = -1.

Step 4: Test the Intervals:
We need to test the intervals between the critical points (-∞, -1), (-1, 6), and (6, ∞) to see where the inequality holds true.

Step 5: Determine the Solution:
- For the interval (-∞, -1):
Substitute p = -2, we get (-2 - 6)(-2 + 1) = (-8)(-1) = 8 > 0 (false)
- For the interval (-1, 6):
Substitute p = 0, we get (0 - 6)(0 + 1) = (-6)(1) = -6 < 0="" />
- For the interval (6, ∞):
Substitute p = 7, we get (7 - 6)(7 + 1) = (1)(8) = 8 > 0 (false)

Conclusion:
The inequality p^2 + 5 < 5p="" +="" 14="" is="" satisfied="" when="" p="" is="" less="" than="" or="" equal="" to="" 6="" and="" greater="" than="" -1.="" therefore,="" the="" correct="" answer="" is="" option="" 'd':="" p="" ≤="" 6,="" p="" /> -1.
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"Alan B. Krueger, first presented what is now widely known as the Great Gatsby Curve, which shows that the higher income inequality is in a society, the more difficult it is for a person to move outside the income class he or she was born into. The British epidemiologist Kate E. Pickett says outcomes such as mental and physical health, drug abuse, education, imprisonment, obesity, social mobility, trust and community, and child well-being are worse for the majority of people in countries where income inequality is high. Across societies, the richest 1% now hold a larger percentage of national income than ever before. What’s puzzling is that the latest research on attitudes toward inequality suggests that citizens in more unequal countries are less concerned about income inequality than those in more egalitarian countries. We also found that increasing an individual’s income only increased life satisfaction if their ranked position also improved. We also found that improvements in an individual’s income rank position bought more happiness in countries where top incomes were concentrated in the hands of a few. So, the more unequal the society, the more moving up the income ladder contributed to someone’s overall well-being.”Q. Which of the following, if true, weakens the author’s conclusion about “attitude toward inequality”?

"Alan B. Krueger, first presented what is now widely known as the Great Gatsby Curve, which shows that the higher income inequality is in a society, the more difficult it is for a person to move outside the income class he or she was born into. The British epidemiologist Kate E. Pickett says outcomes such as mental and physical health, drug abuse, education, imprisonment, obesity, social mobility, trust and community, and child well-being are worse for the majority of people in countries where income inequality is high. Across societies, the richest 1% now hold a larger percentage of national income than ever before. What’s puzzling is that the latest research on attitudes toward inequality suggests that citizens in more unequal countries are less concerned about income inequality than those in more egalitarian countries. We also found that increasing an individual’s income only increased life satisfaction if their ranked position also improved. We also found that improvements in an individual’s income rank position bought more happiness in countries where top incomes were concentrated in the hands of a few. So, the more unequal the society, the more moving up the income ladder contributed to someone’s overall well-being.”Q. What could be inferred from the statement made by Kate?

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The inequality of p2 + 5 < 5p + 14 can be satisfied if:a)p ≥ 6, p = 1b)p = 6, p = −2c)p ≤ 6, p ≤ 1d)p ≤ 6, p > −1Correct answer is option 'D'. Can you explain this answer?
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