Solve the inequality.
$n-11<33$
A. $n<44$
B. $n<22$
C. $n>44$
D. $n>22
Answer (2)
Solve the first inequality: n − 11 < 33 which simplifies to n < 44 .
List all inequalities: n < 44 , n < 44 , n < 22 , 44"> n > 44 , 22"> n > 22 .
Identify conflicting inequalities: n < 44 and 44"> n > 44 cannot be simultaneously true.
Conclude that there is no solution: No solution .
Explanation
Analyze the Inequalities We are given a set of inequalities and we need to find the solution that satisfies all of them. Let's analyze each inequality separately and then find the common solution.
Solve the First Inequality The first inequality is n − 11 < 33 . To solve for n , we add 11 to both sides of the inequality: n − 11 + 11 < 33 + 11
n < 44
List All Inequalities Now we have the following inequalities:
n < 44
n < 44
n < 22
44"> n > 44
22"> n > 22
We need to find the values of n that satisfy all these inequalities simultaneously.
Find the Common Solution Let's analyze the inequalities. We have n < 44 and 44"> n > 44 . These two inequalities cannot be true at the same time. Therefore, there is no solution that satisfies all the given inequalities.
Conclusion Since there is no value of n that can satisfy both n < 44 and 44"> n > 44 simultaneously, the given set of inequalities has no solution.
Examples
Imagine you're trying to plan a trip and you have several constraints: you want to spend less than $500, but also more than $700. These conflicting constraints mean you can't plan the trip as described. Similarly, in our problem, the conflicting inequalities prevent a solution from existing.
The solution to the inequality n − 11 < 33 is n < 44 , which matches option A. This means any value of n that is less than 44 satisfies the inequality. Thus, the chosen answer is A: n < 44 .
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