Question

current skill $ which graph shows the solution set for this inequality? -4 - 8x ≥ 6

Explanation:

Step1: Solve the inequality

$$\begin{align*} -4-8x&\geq6\\ -8x&\geq6 + 4\\ -8x&\geq10\\ x&\leq-\frac{10}{8}\\ x&\leq-\frac{5}{4} \end{align*}$$

Step2: Analyze the solution on the number - line

The solution \(x\leq-\frac{5}{4}\) means that on the number - line, we have a closed circle at \(x =-\frac{5}{4}\) (because the inequality is \(\geq\) and after dividing by a negative number, the direction of the inequality sign changes) and the line extends to the left (towards the negative infinity).

Answer:

The graph with a closed circle at \(-\frac{5}{4}\) and the line extending to the left.