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Answer :
To determine the inequality that represents Alicia's spending situation, let's break down the given details:
1. Alicia's Spending Limit: Alicia has at most [tex]$210 to spend on two items: a new tennis racket and a new tennis net.
2. Understanding "At Most": The phrase "at most" means that the total amount she spends cannot exceed $[/tex]210. So, if we add the cost of the tennis racket (x) and the tennis net (y), this sum should be less than or equal to [tex]$210.
3. Setting Up the Inequality: We need to express this constraint in an inequality. The way to represent that the total cost (x + y) should not exceed $[/tex]210 is using the inequality:
[tex]\[
x + y \leq 210
\][/tex]
4. Choosing the Right Option: Review the given options:
- (A) [tex]\(x + y \leq 210\)[/tex]
- (B) [tex]\(y \leq 210 + x\)[/tex]
- (C) [tex]\(x + y \geq 210\)[/tex]
- (D) [tex]\(y - x \leq 210\)[/tex]
From the breakdown of Alicia's spending limit, option (A) [tex]\(x + y \leq 210\)[/tex] accurately represents the situation where the total cost for both items does not exceed $210.
Therefore, the correct inequality for this situation is option (A), [tex]\(x + y \leq 210\)[/tex].
1. Alicia's Spending Limit: Alicia has at most [tex]$210 to spend on two items: a new tennis racket and a new tennis net.
2. Understanding "At Most": The phrase "at most" means that the total amount she spends cannot exceed $[/tex]210. So, if we add the cost of the tennis racket (x) and the tennis net (y), this sum should be less than or equal to [tex]$210.
3. Setting Up the Inequality: We need to express this constraint in an inequality. The way to represent that the total cost (x + y) should not exceed $[/tex]210 is using the inequality:
[tex]\[
x + y \leq 210
\][/tex]
4. Choosing the Right Option: Review the given options:
- (A) [tex]\(x + y \leq 210\)[/tex]
- (B) [tex]\(y \leq 210 + x\)[/tex]
- (C) [tex]\(x + y \geq 210\)[/tex]
- (D) [tex]\(y - x \leq 210\)[/tex]
From the breakdown of Alicia's spending limit, option (A) [tex]\(x + y \leq 210\)[/tex] accurately represents the situation where the total cost for both items does not exceed $210.
Therefore, the correct inequality for this situation is option (A), [tex]\(x + y \leq 210\)[/tex].
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