Solve the inequality. Graph the solution.

Question

4x+8≥2x+20


(1 point)
Responses

Answer 1

To solve the inequality \(4x + 8 \geq 2x + 20\), we can follow these steps:

1. Subtract \(2x\) from both sides:

   \[ 4x - 2x + 8 \geq 20 \] This simplifies to: \[ 2x + 8 \geq 20 \]

2. Subtract \(8\) from both sides:

   \[ 2x \geq 20 - 8 \] This simplifies to: \[ 2x \geq 12 \]

3. Divide both sides by \(2\):

   \[ x \geq \frac{12}{2} \] Simplifying gives: \[ x \geq 6 \]

The solution to the inequality is \(x \geq 6\).

Graphing the Solution

On a number line, you can represent the solution as follows:

• Draw a number line.
• Shade the region to the right of \(6\).
• Place a closed dot at \(6\) to indicate that \(6\) is included in the solution.

Here is a simple representation:

<---|----|----|----|----|----|----|----|----|----|---->
    4    5    6    7    8    9   10   11   12   13   
                ●==================>

This graph indicates that all values \(x\) greater than or equal to \(6\) are part of the solution to the inequality \(4x + 8 \geq 2x + 20\).