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Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities 2 + x < 6 and 2 −3x < − 1.
- a)1 , 2 , 3
- b)2 , 3
- c)2 , 3, 4,
- d)1 , 2, 3, 4.
Correct answer is option 'B'. Can you explain this answer?
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Given that x is an integer, find the values of x which satisfy the sim...
Given Inequalities:
- 2 + x < 6
- 2 −3x < − 1
Step 1: Solve the first inequality 2 + x < 6
Subtract 2 from both sides:
x < 6 - 2
Simplifying:
x < 4
Thus, from the first inequality, we have:
x < 4
Step 2: Solve the second inequality 2 - 3x < -1
Subtract 2 from both sides:
- 3x < -1 - 2
Simplifying:
- 3x < -3
Now, divide both sides by -3, and remember to reverse the inequality sign when dividing by a negative number:
x > 1
Step 3: Combine the results
From the first inequality, we know x < 4.
From the second inequality, we know x > 1.
Thus, the solution for x must satisfy both:
1 < x < 4
The integer values of xxx that lie between 1 and 4 are:
x = 2, 3
The correct option is: B: 2, 3
Subtract 2 from both sides:
x < 6 - 2
Simplifying:
x < 4
Thus, from the first inequality, we have:
x < 4
Step 2: Solve the second inequality 2 - 3x < -1
Subtract 2 from both sides:
- 3x < -1 - 2
Simplifying:
- 3x < -3
Now, divide both sides by -3, and remember to reverse the inequality sign when dividing by a negative number:
x > 1
Step 3: Combine the results
From the first inequality, we know x < 4.
From the second inequality, we know x > 1.
Thus, the solution for x must satisfy both:
1 < x < 4
The integer values of xxx that lie between 1 and 4 are:
x = 2, 3
The correct option is: B: 2, 3
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Understanding the Inequalities
To solve the simultaneous linear inequalities, we need to work through each inequality separately.
First Inequality: 2 + x < />
- Subtract 2 from both sides:
- x < 6="" -="" />
- x < />
- This means x can take values less than 4.
Second Inequality: 2 - 3x < />
- Subtract 2 from both sides:
- -3x < -1="" -="" />
- -3x < />
- Divide both sides by -3 (remember to flip the inequality sign):
- x > 1
Combining the Results
Now we combine the results of both inequalities:
- From the first inequality: x < />
- From the second inequality: x > 1
Thus, we have:
- 1 < x="" />< />
This means x can take integer values of 2 and 3.
Identifying Possible Values
The integers satisfying the combined inequalities are:
- 2
- 3
Final Answer
These values match with option 'B' which states that the integers satisfying the inequalities are 2 and 3. Hence, the correct answer is option 'B'.
To solve the simultaneous linear inequalities, we need to work through each inequality separately.
First Inequality: 2 + x < />
- Subtract 2 from both sides:
- x < 6="" -="" />
- x < />
- This means x can take values less than 4.
Second Inequality: 2 - 3x < />
- Subtract 2 from both sides:
- -3x < -1="" -="" />
- -3x < />
- Divide both sides by -3 (remember to flip the inequality sign):
- x > 1
Combining the Results
Now we combine the results of both inequalities:
- From the first inequality: x < />
- From the second inequality: x > 1
Thus, we have:
- 1 < x="" />< />
This means x can take integer values of 2 and 3.
Identifying Possible Values
The integers satisfying the combined inequalities are:
- 2
- 3
Final Answer
These values match with option 'B' which states that the integers satisfying the inequalities are 2 and 3. Hence, the correct answer is option 'B'.
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Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities2+x<6 and 2−3x<−1.a)1 , 2 , 3b)2 , 3c)2 , 3, 4,d)1 , 2, 3, 4.Correct answer is option 'B'. 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 Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities2+x<6 and 2−3x<−1.a)1 , 2 , 3b)2 , 3c)2 , 3, 4,d)1 , 2, 3, 4.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities2+x<6 and 2−3x<−1.a)1 , 2 , 3b)2 , 3c)2 , 3, 4,d)1 , 2, 3, 4.Correct answer is option 'B'. Can you explain this answer?.
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