verifying solutions to inequalities 2(x-4)+x≥8; is -2 a solution

Let's verify if \( x = -2 \) is a solution to the inequality \( 2(x - 4) + x \geq 8 \).

### Step 1: Substitute \( x = -2 \) into the inequality.

The inequality is:
\[
2(x - 4) + x \geq 8
\]

Substitute \( x = -2 \) into this expression:

\[
2(-2 - 4) + (-2) \geq 8
\]

### Step 2: Simplify the expression.

First, simplify inside the parentheses:
\[
2(-6) + (-2) \geq 8
\]

Now, multiply:
\[
-12 - 2 \geq 8
\]

Simplify:
\[
-14 \geq 8
\]

### Step 3: Evaluate the result.

Clearly, \( -14 \) is not greater than or equal to \( 8 \).

### Conclusion:
Since \( -14 \geq 8 \) is false, \( x = -2 \) is **not** a solution to the inequality.

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Would you like more details or have any further questions? Here are some related questions you might explore:

1. How do you solve linear inequalities step by step?
2. What is the difference between solving inequalities and solving equations?
3. How can you graph the solution of an inequality on a number line?
4. Can inequalities have multiple solutions, and how do you represent them?
5. How do you solve compound inequalities (e.g., two inequalities combined)?

**Tip:** Always check your solution by substituting back into the original inequality to ensure correctness.

Learn how to verify if x = -2 is a solution to the inequality 2(x-4) + x ≥ 8. This step-by-step solution simplifies the inequality, using key algebraic concepts like substitution and properties of inequalities. Perfect for students in Grades 7-9.

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