y = 4 - (x + 7) + 2x and y is at least 9.

You are given the equation \( y = 4 - (x + 7) + 2x \), and you are told that \( y \) is at least 9. We can now solve this inequality step by step.

### Step 1: Simplify the expression for \( y \).
Let's first simplify the right-hand side:

\[
y = 4 - (x + 7) + 2x
\]

Distribute the negative sign across the parentheses:

\[
y = 4 - x - 7 + 2x
\]

Combine like terms:

\[
y = -x + 2x + 4 - 7
\]

\[
y = x - 3
\]

Now the equation is:

\[
y = x - 3
\]

### Step 2: Set up the inequality.
We are given that \( y \) is at least 9, meaning \( y \geq 9 \). Substitute \( y = x - 3 \) into this inequality:

\[
x - 3 \geq 9
\]

### Step 3: Solve for \( x \).
Add 3 to both sides of the inequality:

\[
x \geq 12
\]

### Conclusion:
The solution to the inequality is \( x \geq 12 \).

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

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Here are 5 related questions:
1. What happens to the graph of \( y = x - 3 \) when \( y \geq 9 \)?
2. How does the inequality \( x \geq 12 \) change if the original equation were different, like \( y = x + 5 \)?
3. What would the solution be if \( y \) were less than or equal to 9 instead?
4. How does the inequality change if we introduce absolute values, such as \( y = |x - 3| \geq 9 \)?
5. What would the graph of \( y = x - 3 \) look like, and how would the solution \( x \geq 12 \) be represented?

**Tip:** Always check if an equation can be simplified before solving the inequality to avoid unnecessary complexity.

Learn how to solve the linear inequality y = 4 - (x + 7) + 2x, where y is at least 9, with a step-by-step breakdown. Understand key algebraic concepts like simplifying expressions and solving inequalities. Suitable for students in Grades 6-8.

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