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Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15?
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Find the range of real values of x satisfying the inequalities 3x-2 >7...
Finding the Range of Real Values of x Satisfying Inequalities
- Understanding the Inequalities:
- The inequality 3x-2 >7 means that the expression 3x-2 is greater than 7. This can be written as:
- The inequality 4x-13>15 means that the expression 4x-13 is greater than 15. This can be written as:
- Solving the Inequalities:
- For the first inequality, we add 2 to both sides:
- Then, we divide both sides by 3:
- This means that any value of x greater than 3 will satisfy the first inequality.
- For the second inequality, we add 13 to both sides:
- Then, we divide both sides by 4:
- This means that any value of x greater than 7 will satisfy the second inequality.
- Combining the Solutions:
- The solution set for the first inequality is x >3.
- The solution set for the second inequality is x >7.
- The intersection of these solution sets is x >7, since any value of x greater than 7 will satisfy both inequalities.
- Final Answer:
Before solving the inequalities, it is important to understand what they mean:
3x-2 >7
4x-13>15
To solve the inequalities, we need to isolate x on one side of the inequality sign:
3x-2+2 >7+2
3x >9
3x/3 >9/3
x >3
4x-13+13 >15+13
4x >28
4x/4 >28/4
x >7
To find the range of real values of x that satisfy both inequalities, we need to find the intersection of the two solution sets:
The range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15 is:
x >7
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Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15?
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Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15?.
Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the range of real values of x satisfying the inequalities 3x-2 >7 and 4x-13>15?.
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