Question

1. what does the solution to $x + 4>6$ look like on a number line?

a. open circle at 2, shading to the left
b. open circle at 2, shading to the right
c. closed circle at 2, shading to the left
d. closed circle at 2, shading to the right

Explanation:

Step1: Solve the inequality

$$\begin{align*} x + 4&>6\\ x+4 - 4&>6 - 4\\ x&>2 \end{align*}$$

Step2: Analyze the number - line representation

Since \(x>2\), we use an open circle at \(x = 2\) (because \(2\) is not included in the solution set). And for \(x>2\), the values of \(x\) are greater than \(2\), so we shade to the right of \(2\) on the number line.

Answer:

B. Open circle at 2, shading to the right