Solve and graph this inequality: 3-x/2 ≤2

Answer 1

To solve the inequality \( 3 - \frac{x}{2} \leq 2 \), we can follow these steps:

1. Isolate the term involving \( x \):

   Subtract 3 from both sides:

   \[ 3 - \frac{x}{2} - 3 \leq 2 - 3 \]

   This simplifies to:

   \[ -\frac{x}{2} \leq -1 \]

2. Eliminate the negative sign:

   We can multiply both sides by -1, but remember to reverse the inequality sign:

   \[ \frac{x}{2} \geq 1 \]

3. Solve for \( x \):

   Multiply both sides by 2:

   \[ x \geq 2 \]

So the solution to the inequality is \( x \geq 2 \).

Graphing the Inequality

To graph this inequality on a number line:

1. Draw a number line.
2. Mark the point \( 2 \) on the number line.
3. Since the inequality is \( x \geq 2 \), we will use a closed circle at 2 to indicate that 2 is included in the solution.
4. Shade the line to the right of 2 to show all numbers greater than 2.

Here is a simple representation of the number line:

---|---|---|---|---|---|---|---|---|---|---
...  0   1   2   3   4   5   6   7   8   9 ...
      ●========================>

The filled circle at \( 2 \) represents that \( 2 \) is included in the solution, and the shaded area to the right indicates all numbers greater than \( 2 \).