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If 3x + 22x ≥ 5x, then the solution set for x is:
- a)(-∞, 2]
- b)[2, ∞)
- c)[0, 2]
- d){2}
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If 3x + 22x ≥ 5x, then the solution set for x is:a)(-∞, 2]b)[...
We have,
3x + 22x ≥ 5x
⇒ (3/5)x + (4/5)x ≥ 1
⇒ (3/5)x + (4/5)x ≥ (3/5)2 + (4/5)2
⇒ x ≤ 2 ⇒ x ∈ (-∞, 2]
[If ax + bx ≥ 1 and a2 + b2 = 1], then x ∈ (-∞, 2)
3x + 22x ≥ 5x
⇒ (3/5)x + (4/5)x ≥ 1
⇒ (3/5)x + (4/5)x ≥ (3/5)2 + (4/5)2
⇒ x ≤ 2 ⇒ x ∈ (-∞, 2]
[If ax + bx ≥ 1 and a2 + b2 = 1], then x ∈ (-∞, 2)
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Community Answer
If 3x + 22x ≥ 5x, then the solution set for x is:a)(-∞, 2]b)[...
Understanding the Inequality
To solve the inequality 3x + 22x ≥ 5x, we first simplify the left side:
- Combine like terms: 3x + 22x = 25x.
- The inequality then becomes: 25x ≥ 5x.
Simplifying the Inequality
Next, we isolate x:
- Subtract 5x from both sides: 25x - 5x ≥ 0.
- This simplifies to: 20x ≥ 0.
Finding the Solution Set
Now, we can solve for x:
- Divide both sides by 20: x ≥ 0.
This means that x can be any value greater than or equal to 0.
Interpreting the Solution Set
The solution set consists of all real numbers starting from 0 and extending to positive infinity. Therefore, we can express this solution set in interval notation:
- The interval is [0, +∞).
Conclusion
Given the options provided:
- a) [0, ∞) - This is correct.
- b) (-∞, 2] - Incorrect as it includes negative values.
- c) [0, 2] - Incorrect as it limits the upper bound.
- d) (-2, ∞) - Incorrect as it includes negative values.
Thus, the correct answer is option 'A':
[0, ∞).
To solve the inequality 3x + 22x ≥ 5x, we first simplify the left side:
- Combine like terms: 3x + 22x = 25x.
- The inequality then becomes: 25x ≥ 5x.
Simplifying the Inequality
Next, we isolate x:
- Subtract 5x from both sides: 25x - 5x ≥ 0.
- This simplifies to: 20x ≥ 0.
Finding the Solution Set
Now, we can solve for x:
- Divide both sides by 20: x ≥ 0.
This means that x can be any value greater than or equal to 0.
Interpreting the Solution Set
The solution set consists of all real numbers starting from 0 and extending to positive infinity. Therefore, we can express this solution set in interval notation:
- The interval is [0, +∞).
Conclusion
Given the options provided:
- a) [0, ∞) - This is correct.
- b) (-∞, 2] - Incorrect as it includes negative values.
- c) [0, 2] - Incorrect as it limits the upper bound.
- d) (-2, ∞) - Incorrect as it includes negative values.
Thus, the correct answer is option 'A':
[0, ∞).
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If 3x + 22x ≥ 5x, then the solution set for x is:a)(-∞, 2]b)[2, ∞)c)[0, 2]d){2}Correct answer is option 'A'. Can you explain this answer? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about If 3x + 22x ≥ 5x, then the solution set for x is:a)(-∞, 2]b)[2, ∞)c)[0, 2]d){2}Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3x + 22x ≥ 5x, then the solution set for x is:a)(-∞, 2]b)[2, ∞)c)[0, 2]d){2}Correct answer is option 'A'. Can you explain this answer?.
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