Question

Look at the inequality below.

-2x+4≥0

Which of the following represents the solution to the inequality?

Answer 1

number line

Answer 2

To solve the inequality \(-2x + 4 \geq 0\), follow these steps:

1. **Subtract 4 from both sides:**
\[
-2x \geq -4
\]

2. **Divide both sides by -2 (remember to reverse the inequality sign when dividing by a negative number):**
\[
x \leq 2
\]

So, the solution to the inequality \(-2x + 4 \geq 0\) is \(x \leq 2\).

This means that the values of \(x\) that satisfy the inequality are all real numbers less than or equal to 2.

Answer 3

To represent the solution \( x \leq 2 \) on a number line, you can follow these steps:

1. **Draw a horizontal line**: This represents your number line.

2. **Mark and label some key points**: Include the point \(2\) and a few points before and after it (for example, \(0\), \(1\), \(2\), \(3\), and \(4\)).

3. **Draw a closed circle at the point \(2\)**: The closed circle indicates that \(2\) is included in the solution set (since the inequality is "less than or equal to").

4. **Shade to the left of \(2\)**: This shading represents all the numbers that are less than \(2\).

Here’s how it should look visually:

```
---|---|---|---|---|---|---|---|---|---
0 1 2 3 4

<------●
```

The closed circle at \(2\) indicates that \(2\) is part of the solution, and the arrow pointing to the left represents all numbers less than \(2\).