Question

1. which number line represents the solution to the inequality 9 - 4x ≥ 17?

Explanation:

Step1: Solve the inequality

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Divide both sides by - 4. When dividing an inequality by a negative number, the direction of the inequality sign changes. So \(x\leq - 2\).

Step2: Analyze number - line representations

On a number - line, for \(x\leq - 2\), we have a closed circle at - 2 (because the inequality includes equality) and the line extends to the left.

Answer:

We need to find the number - line with a closed circle at - 2 and the line extending to the left. Without seeing the specific details of the endpoints and circles on each number - line in the options, if we assume the number - lines are labeled with appropriate values and the circles and arrows are standard representations, the correct number - line will have a closed circle at a value corresponding to - 2 and an arrow pointing to the left. If we assume the number - lines are labeled with values like - 5, 0, 5 etc. and the intervals are consistent, we look for a closed circle at the value that represents - 2 and an arrow going left. If we had to make a general choice based on the description of the solution \(x\leq - 2\), we would choose the number - line that has a closed circle at the appropriate negative value (presumably - 2) and an arrow pointing left. But since we have no specific details about the number - lines in the options other than their general form, we can't definitively say which of A, B, C, D it is. If we assume standard number - line labeling and representation, we need to find the one with a closed circle at - 2 and arrow left.