The problem describes the number of adoptions that occurred each week for three weeks. We are given: - Week 1: $x$ adoptions - Week 2: $x + 10$ adoptions - Week 3: $2x$ adoptions The total number of adoptions over the three weeks is at least 50. We need to find the inequality that represents all possible values of $x$.

1. Problem Description

The problem describes the number of adoptions that occurred each week for three weeks. We are given:

- Week 1: $x$ adoptions

- Week 2: $x + 10$ adoptions

- Week 3: $2x$ adoptions

The total number of adoptions over the three weeks is at least

5

0. We need to find the inequality that represents all possible values of $x$.

2. Solution Steps

First, we can write an expression for the total number of adoptions over the three weeks by summing the adoptions in each week:

$x + (x + 10) + 2x$

This simplifies to:

$4x + 10$

We are given that the total number of adoptions is at least

5

0. This means:

$4x + 10 \ge 50$

3. Final Answer

The inequality that represents all possible values of $x$ is $4x + 10 \ge 50$.

So the correct answer is option B.