https://r2.erweima.ai/mathbot/image/17268584428070ptjq3uh.jpg

The inequality extracted from the image is:

\[
17 + 3x - (x + 2) \geq 4 - x
\]

Now, let's solve this step by step.

### Step 1: Simplify both sides
Expand the left-hand side:
\[
17 + 3x - (x + 2) = 17 + 3x - x - 2 = 15 + 2x
\]

So the inequality becomes:
\[
15 + 2x \geq 4 - x
\]

### Step 2: Move all terms involving \( x \) to one side
Add \( x \) to both sides:
\[
15 + 2x + x \geq 4
\]
\[
15 + 3x \geq 4
\]

### Step 3: Isolate the \( x \) term
Subtract 15 from both sides:
\[
3x \geq 4 - 15
\]
\[
3x \geq -11
\]

### Step 4: Solve for \( x \)
Divide both sides by 3:
\[
x \geq \frac{-11}{3}
\]

Thus, the solution to the inequality is:
\[
x \geq -\frac{11}{3}
\]

Would you like further clarification or additional steps?

Here are some related questions:
1. What is the difference between solving inequalities and equations?
2. How does reversing the inequality sign work when multiplying/dividing by a negative number?
3. Can you apply the same steps to solve compound inequalities?
4. What is the graphical interpretation of this inequality?
5. How do you check whether a value satisfies an inequality?

**Tip**: Always double-check that the inequality direction remains correct when performing operations, especially when multiplying or dividing by negative numbers.

Learn how to solve the linear inequality 17 + 3x - (x + 2) ≥ 4 - x step by step. This problem covers core algebraic concepts and inequality manipulation. Suitable for students in Grades 8-10.

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