Question

which number line shows the solution for the inequality? 17 ≥ 1 - 4b

Explanation:

Answer:

B. A number - line with a closed circle at - 4 and an arrow pointing to the right

1. First, solve the inequality \(17\geq1 - 4b\):

• Subtract 1 from both sides: \(17−1\geq1 - 4b-1\), which simplifies to \(16\geq - 4b\).
• Divide both sides by - 4. When dividing an inequality by a negative number, the direction of the inequality sign changes. So, \(\frac{16}{-4}\leq\frac{-4b}{-4}\), which gives \(b\geq - 4\).

1. Then, represent the solution on a number - line:

• The solution \(b\geq - 4\) is represented by a closed circle at - 4 (because the inequality is \(\geq\), meaning - 4 is included in the solution set) and an arrow pointing to the right. This matches option B.