Question

solve the inequality and graph the solution.
3 ≤ -(b - 7)
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Simplify the inequality

$$3\leq-(b - 7)$$
Expand the right - hand side: $$3\leq - b+7$$

Step2: Isolate the variable \(b\)

Subtract \(7\) from both sides: $$3 - 7\leq - b+7 - 7$$
$$- 4\leq - b$$
Multiply both sides by \(-1\) (and reverse the inequality sign): $$4\geq b$$ or \(b\leq4\)

Answer:

The solution of the inequality \(3\leq-(b - 7)\) is \(b\leq4\). On the number line, we plot a closed circle at \(4\) (since the inequality is \(\leq\)) and draw a ray to the left.