For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, $e$?
A. $e \geq 50$ or $e \leq 100$
B. $e>50$ or $e<100$
C. $50 < e < 100$
D. $50 \leq e \leq 100$
Answer (2)
Dexter's earnings are no less than 50 , w hi c h t r an s l a t es t o e \geq 50$.
Dexter's earnings are no more than 100 , w hi c h t r an s l a t es t o e \leq 100$.
Combining these, the inequality representing his earnings is 50 ≤ e ≤ 100 .
Therefore, the correct inequality is 50 ≤ e ≤ 100 .
Explanation
Understanding the Problem Let's analyze the problem. Dexter's earnings, represented by e , have a minimum value of $50 and a maximum value of $100. We need to express this range as a single inequality.
Expressing the Minimum Earnings The phrase 'no less than $50' means that Dexter's earnings are greater than or equal to 50. T hi sc anb e w r i tt e na s : e g e 50 $
Expressing the Maximum Earnings The phrase 'no more than $100' means that Dexter's earnings are less than or equal to 100. T hi sc anb e w r i tt e na s : e l e 100 $
Combining the Inequalities Combining these two inequalities, we get: 50 l ee l e 100 This means that e is between $50 and $100, inclusive.
Final Answer Therefore, the inequality that represents Dexter's earnings is $50
le e
le 100$.
Examples
Understanding inequalities is very useful in everyday life. For example, when you're budgeting your monthly expenses, you might set a limit on how much you spend on entertainment. If you want to spend 'no more than' 100 o n e n t er t ainm e n t , yo u c an re p rese n t yo u rs p e n d in g , s , w i t h t h e in e q u a l i t y s \leq 100$. This helps you keep track of your spending and stay within your budget. Similarly, if you want to save 'at least' 50 e a c hm o n t h , yo u c an re p rese n t yo u rs a v in g s , v , w i t h t h e in e q u a l i t y v \geq 50$.
The inequality that represents Dexter's earnings is 50 ≤ e ≤ 100 , meaning his earnings are at least $50 and at most $100. This encompasses both bounds of his earnings effectively. Therefore, the correct answer is option D.
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