Let's solve the given inequality step by step.

The inequality is:

$22 \geq 5(2y + 3) - 3y$

Step 1: Expand the expression on the right-hand side.

Distribute the $5$ over the terms inside the parentheses:

$5(2y + 3) = 10y + 15$

So, the inequality becomes:

$22 \geq 10y + 15 - 3y$

Step 2: Combine like terms.

Now, combine the terms involving $y$:

$10y - 3y = 7y$

This simplifies the inequality to:

$22 \geq 7y + 15$

Step 3: Solve for $y$.

First, subtract 15 from both sides:

$22 - 15 \geq 7y$ $7 \geq 7y$

Next, divide both sides by 7:

$1 \geq y$

or equivalently:

$y \leq 1$

Step 4: Graph the inequality.

The solution is $y \leq 1$, which means all values of $y$ less than or equal to 1. On a number line, this would be represented by a closed circle at $1$ with an arrow extending to the left (since $y$ is less than or equal to 1).

Final Answer:

• The correct answer for the inequality is $y \leq 1$.
• The graph should show a closed circle at $1$ and a line extending to the left, covering values less than or equal to 1.

Would you like more details, or do you have any other questions?

Here are five follow-up questions based on this:

1. How do you solve inequalities with multiple steps?
2. What happens if you multiply or divide an inequality by a negative number?
3. How would the solution change if the inequality symbol was reversed?
4. How can you check if a given value is a solution to an inequality?
5. What is the difference between solving an equation and solving an inequality?

Tip: When graphing inequalities, always pay attention to whether the inequality is strict (< or >) or inclusive (≤ or ≥) for determining open or closed circles on the graph.