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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.

Solve the inequality for y: 4 ≤ -2(5 - y) + 5y

Learn how to solve the linear inequality 4 ≤ -2(5 - y) + 5y with a clear step-by-step solution. This problem explores key algebraic concepts and properties of inequalities. Suitable for students in Grades 8-10.

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