Let's carefully examine the problem to find the correct condition for a shopper to qualify for the [tex]$10\%$[/tex] discount.
1. Understand the Requirement: According to the problem, to get the [tex]$10\%$[/tex] discount, a shopper must spend no less than [tex]$400$[/tex] dollars.
2. Define the Variable: Let [tex]\( d \)[/tex] represent the spending (in dollars) of a shopper who gets the discount. The condition here is that the spending should be no less than [tex]$400.
3. Form the Inequality: The phrase "no less than" means that the amount \( d \) must be greater than or equal to $[/tex]400[tex]$. This translates mathematically to the inequality:
\[
d \geq 400
\]
4. Verification: If a shopper spends exactly $[/tex]400[tex]$, they will be eligible for the discount. If a shopper spends more than $[/tex]400[tex]$, they will also be eligible. Hence, our inequality correctly encapsulates both possibilities.
Therefore, the inequality that represents the condition for a shopper to qualify for the $[/tex]10\%$ discount is:
[tex]\[
d \geq 400
\][/tex]
