Question

1. consider the given inequality that models the least amount of steps needed to earn a \gold medal\ badge in a fitness challenge, where:

• $w$ represents the number of steps recorded from the weekend.
• $s$ represents the number of steps walked each day of the work week.
• $x$ represents the number of days during the work week needed to walk.

$w + sx \geq 25000$

enter an inequality for which the solution is the least amount of days javier needs to walk if javier already has 7000 steps recorded from the weekend and he plans to walk 3500 steps each day of the work week.

Explanation:

Step1: Substitute given values

Substitute $w=7000$ and $s=3500$ into the inequality.
$7000 + 3500x \geq 25000$

Step2: Isolate the term with $x$

Subtract 7000 from both sides.
$3500x \geq 25000 - 7000$
$3500x \geq 18000$

Step3: Solve for $x$

Divide both sides by 3500.
$x \geq \frac{18000}{3500}$
$x \geq \frac{36}{7} \approx 5.14$
Since $x$ represents days, we use the inequality in terms of $x$ that shows the minimum days needed.

Answer:

$7000 + 3500x \geq 25000$ (or simplified to $3500x \geq 18000$ or $x \geq \frac{36}{7}$)