Question

question 1 - 3
which graph shows the solution to the inequality $-2(2x + 3)\leq26$?

Explanation:

Step1: Solve the inequality

$$\begin{align*} -2(2x + 3)&\leq26\\ -4x-6&\leq26\\ -4x&\leq26 + 6\\ -4x&\leq32\\ x&\geq\frac{32}{-4}\\ x&\geq - 8 \end{align*}$$

Step2: Analyze the graph

The solution \(x\geq - 8\) means that the graph should have a closed - circle at \(x = - 8\) (because the inequality is \(\geq\), including the equal part) and the line should extend to the right (towards larger values of \(x\)).

Answer:

The first option (the graph with a closed - circle at \(x=-8\) and the line extending to the right) is the correct graph.