Question

solve the inequality and graph the solution.
-1 ≤ b + 5
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.
save answer

Explanation:

Step1: Isolate the variable \( b \)

Subtract \( 5 \) from both sides of the inequality \( -1\leq b + 5 \).
Using the subtraction property of inequalities: \( -1-5\leq b+5 - 5 \).
Simplify the left - hand side: \( -6\leq b \), which can be rewritten as \( b\geq - 6 \).

Step2: Graph the solution

On the number line, since the inequality is \( b\geq - 6 \), we place a closed circle at \( -6 \) (because the inequality includes equality, i.e., \( \leq \) or \( \geq \) means the endpoint is included). Then we draw a ray to the right (because \( b \) is greater than or equal to \( -6 \)).

Answer:

The solution of the inequality is \( b\geq - 6 \). On the number line, there is a closed circle at \( -6 \) and a ray extending to the right.