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What are the values of x for which (x + 2)(x + 3) >, 0 holds true?
- a)for all real values
- b)x > - 2
- c)x < - 3
- d)x < - 3 or x > - 2
Correct answer is option 'D'. Can you explain this answer?
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What are the values of x for which (x + 2)(x + 3) >, 0 holds true?a...
Take random number in each option and solve for x. Eliminate those which fail in holding given inequality true.
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What are the values of x for which (x + 2)(x + 3) >, 0 holds true?a...
Understanding the Inequality:
The inequality given is (x + 2)(x + 3) > 0. To solve this inequality, we need to find the values of x for which the product of (x + 2) and (x + 3) is greater than zero.
Analysis:
- In order for the product of two numbers to be greater than zero, either both numbers must be positive or both must be negative.
- If both numbers are positive, the inequality will hold true.
- If both numbers are negative, the inequality will also hold true since the product of two negative numbers is positive.
Solving the Inequality:
- To find the values of x for which the inequality holds true, we need to consider the possible cases:
- Case 1: Both (x + 2) and (x + 3) are positive. This occurs when x > -2.
- Case 2: Both (x + 2) and (x + 3) are negative. This occurs when x < />
Combining the Cases:
- The values of x that satisfy the inequality are those that fall into either Case 1 or Case 2.
- Therefore, the values of x for which (x + 2)(x + 3) > 0 holds true are x < -3="" or="" x="" /> -2.
Conclusion:
Hence, the correct answer is option 'D' - x < -3="" or="" x="" /> -2. This answer considers all possible cases and provides a comprehensive explanation for the values of x for which the given inequality is true.
The inequality given is (x + 2)(x + 3) > 0. To solve this inequality, we need to find the values of x for which the product of (x + 2) and (x + 3) is greater than zero.
Analysis:
- In order for the product of two numbers to be greater than zero, either both numbers must be positive or both must be negative.
- If both numbers are positive, the inequality will hold true.
- If both numbers are negative, the inequality will also hold true since the product of two negative numbers is positive.
Solving the Inequality:
- To find the values of x for which the inequality holds true, we need to consider the possible cases:
- Case 1: Both (x + 2) and (x + 3) are positive. This occurs when x > -2.
- Case 2: Both (x + 2) and (x + 3) are negative. This occurs when x < />
Combining the Cases:
- The values of x that satisfy the inequality are those that fall into either Case 1 or Case 2.
- Therefore, the values of x for which (x + 2)(x + 3) > 0 holds true are x < -3="" or="" x="" /> -2.
Conclusion:
Hence, the correct answer is option 'D' - x < -3="" or="" x="" /> -2. This answer considers all possible cases and provides a comprehensive explanation for the values of x for which the given inequality is true.
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