Answer :
To determine how much money Harry needs to receive for his birthday in order to afford the smartphone, follow these steps:
1. Harry already has \[tex]$220 in his bank account. The smartphone costs \$[/tex]510. Therefore, the total amount of money Harry will have is the sum of his current money and the birthday money, which is represented by [tex]$x$[/tex].
2. For Harry to be able to afford the smartphone, his total money must be at least \[tex]$510. This relationship can be written as the inequality:
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$
3. Next, subtract 220 from both sides of the inequality to determine the minimum birthday money he needs:
$[/tex][tex]$
x \geq 510 - 220,
$[/tex][tex]$
which simplifies to:
$[/tex][tex]$
x \geq 290.
$[/tex][tex]$
Thus, the correct inequality that models the situation is
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$
In summary, the birthday sum $[/tex]x[tex]$ must be at least \$[/tex]290, so the correct option is the first one.
1. Harry already has \[tex]$220 in his bank account. The smartphone costs \$[/tex]510. Therefore, the total amount of money Harry will have is the sum of his current money and the birthday money, which is represented by [tex]$x$[/tex].
2. For Harry to be able to afford the smartphone, his total money must be at least \[tex]$510. This relationship can be written as the inequality:
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$
3. Next, subtract 220 from both sides of the inequality to determine the minimum birthday money he needs:
$[/tex][tex]$
x \geq 510 - 220,
$[/tex][tex]$
which simplifies to:
$[/tex][tex]$
x \geq 290.
$[/tex][tex]$
Thus, the correct inequality that models the situation is
$[/tex][tex]$
x + 220 \geq 510.
$[/tex][tex]$
In summary, the birthday sum $[/tex]x[tex]$ must be at least \$[/tex]290, so the correct option is the first one.