Question

Question

Solve the inequality. Graph the solution.

4x+8≥2x+20
4
𝑥
+
8
≥
2
𝑥
+
20

(1 point)
Responses

Answer 1

To solve the inequality \( 4x + 8 \geq 2x + 20 \), we can start by isolating the variable \( x \).

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

   \[ 4x - 2x + 8 \geq 20 \]

   This simplifies to:

   \[ 2x + 8 \geq 20 \]

2. Next, subtract 8 from both sides:

   \[ 2x \geq 20 - 8 \]

   This simplifies to:

   \[ 2x \geq 12 \]

3. Now, divide both sides by 2:

   \[ x \geq 6 \]

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

Graphing the solution:

To graph this inequality on a number line:

• Draw a number line.
• Mark the point 6 on the line.
• Since the inequality includes \( x = 6 \) (the inequality is "greater than or equal to"), draw a closed dot at 6.
• Shade the line to the right of 6 to indicate that all values greater than 6 are included in the solution.

The final representation shows the solution to the inequality \( 4x + 8 \geq 2x + 20 \) as \( x \geq 6 \).