Question

question 1 - 3
which graph shows the solution to the inequality $-2(2x + 3) \leq 26$?

Explanation:

Step1: Solve the inequality

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

In the number - line representation of inequalities, if \(x\geq a\) (where \(a=-8\) here), we have a closed - circle at \(a\) (because the inequality is non - strict, i.e., \(\geq\)) and the arrow points to the right (towards the larger values of \(x\)).

Answer:

The graph with a closed - circle at \(x = - 8\) and an arrow pointing upwards (assuming the vertical axis is the \(x\) - axis in the given context, which is a bit non - standard as usually number - lines are horizontal, but based on the direction of the arrow in the provided options, if we consider the vertical axis as the \(x\) - axis) is the correct one.