Question

which number line shows the correct solution to -4x + 8 - 6x ≤ 59 + 7x?

Explanation:

Step1: Solve the inequality

$$\begin{align*} -4x + 8-6x&\leq59 + 7x\\ -4x-6x-7x&\leq59 - 8\\ -17x&\leq51\\ x&\geq - 3 \end{align*}$$

Step2: Analyze the number - line representation

For \(x\geq - 3\), there is a closed circle at \(x = - 3\) (because the inequality is \(\geq\), including the equal part) and the arrow points to the right (towards larger values of \(x\)).

Answer:

The number - line with a closed circle at \(x=-3\) and an arrow pointing to the right (the first non - fully visible number - line in the left with a closed circle at \(x = - 3\) and the arrow direction consistent with \(x\geq - 3\)) is the correct one.