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The solution set for (x + 3) + 4 > − 2x + 5 :
- a)(2 , ∞)
- b)(- ∞ , - 2)
- c)(-2/3, ∞)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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The solution set for(x+3)+4>−2x+5 :a)(2 ,∞)b)(-∞,...
Understanding the Inequality
To solve the inequality (x + 3) + 4 > -2x + 5, we will first simplify both sides.
Step 1: Simplify the Left Side
- Combine like terms:
- (x + 3) + 4 = x + 7
Step 2: Set the Inequality
- The inequality now reads:
- x + 7 > -2x + 5
Step 3: Rearranging the Inequality
- Add 2x to both sides:
- x + 2x + 7 > 5
- This simplifies to:
- 3x + 7 > 5
Step 4: Isolate x
- Subtract 7 from both sides:
- 3x > 5 - 7
- 3x > -2
- Now, divide by 3:
- x > -2/3
Final Solution Set
- The solution set for x is:
- (-2/3, ∞)
Conclusion
- Therefore, the correct answer is option C: (-2/3, ∞).
This means that any value greater than -2/3 will satisfy the inequality. This interval excludes -2/3 itself, hence it starts from -2/3 and extends to positive infinity.
To solve the inequality (x + 3) + 4 > -2x + 5, we will first simplify both sides.
Step 1: Simplify the Left Side
- Combine like terms:
- (x + 3) + 4 = x + 7
Step 2: Set the Inequality
- The inequality now reads:
- x + 7 > -2x + 5
Step 3: Rearranging the Inequality
- Add 2x to both sides:
- x + 2x + 7 > 5
- This simplifies to:
- 3x + 7 > 5
Step 4: Isolate x
- Subtract 7 from both sides:
- 3x > 5 - 7
- 3x > -2
- Now, divide by 3:
- x > -2/3
Final Solution Set
- The solution set for x is:
- (-2/3, ∞)
Conclusion
- Therefore, the correct answer is option C: (-2/3, ∞).
This means that any value greater than -2/3 will satisfy the inequality. This interval excludes -2/3 itself, hence it starts from -2/3 and extends to positive infinity.
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The solution set for(x+3)+4>−2x+5 :a)(2 ,∞)b)(-∞, - 2)c)(-2/3,∞)d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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