The inequality you provided is:

$4 \leq -2(5 - y) + 5y$

Let's solve this step by step.

Step 1: Distribute $-2$ across the terms inside the parentheses.

$-2(5 - y) = -10 + 2y$

So the inequality becomes:

$4 \leq -10 + 2y + 5y$

Step 2: Combine like terms.

$4 \leq -10 + 7y$

Step 3: Isolate the variable $y$.

Add 10 to both sides:

$4 + 10 \leq 7y$

$14 \leq 7y$

Step 4: Solve for $y$.

Divide both sides by 7:

$\frac{14}{7} \leq y$

$2 \leq y$

This means that $y \geq 2$.

Final Answer:

$y \geq 2$

Would you like further explanation on any step?

Here are 5 related questions to expand your understanding:

1. How do you solve inequalities involving fractions?
2. What changes when multiplying or dividing both sides of an inequality by a negative number?
3. How can you graph the solution of this inequality on a number line?
4. How do you solve compound inequalities with "and" or "or" conditions?
5. How do inequalities differ from equations in terms of their properties?

Tip: When solving inequalities, always reverse the inequality sign if you multiply or divide both sides by a negative number.