Consider the following inequality:

−2x+4≥−8
Step 1 of 2 :  Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.


Let's solve the inequality step by step:

Given inequality:
\[
-2x + 4 \geq -8
\]

### Step 1: Isolate the term with \(x\)
First, subtract 4 from both sides of the inequality:
\[
-2x + 4 - 4 \geq -8 - 4
\]
This simplifies to:
\[
-2x \geq -12
\]

### Step 2: Solve for \(x\)
Now, divide both sides by \(-2\). Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips:
\[
x \leq \frac{-12}{-2}
\]
\[
x \leq 6
\]

### Final answer:
\[
x \leq 6
\]

Let me know if you'd like more details or have any questions!

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Here are five related questions to expand your understanding:

1. How does the solution change if we reverse the inequality \( -2x + 4 \leq -8 \)?
2. What happens when multiplying or dividing an inequality by a negative number?
3. How would you express the solution on a number line?
4. Can you write the solution in interval notation?
5. How would you verify if a given value of \(x\) satisfies the inequality?

**Tip:** Always flip the inequality sign when multiplying or dividing by a negative number!

Consider the following inequality: −2x+4≥−8. Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notation.

Learn how to solve the linear inequality −2x + 4 ≥ −8 with a detailed, step-by-step breakdown. This algebraic problem covers key concepts such as solving inequalities and the rule of flipping the inequality sign when dividing by a negative number. Ideal for students in Grades 7-9.

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