Question

solve the inequality and graph the solution. 57 ≥ q + 54 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: Isolate the variable \( q \)

Subtract \( 54 \) from both sides of the inequality \( 57\geq q + 54 \).
Using the subtraction property of inequalities: \( 57-54\geq q+54 - 54 \).
So, \( 3\geq q \), which can be rewritten as \( q\leq3 \).

Step2: Graph the solution

On the number - line, since the inequality is \( q\leq3 \), we place a closed circle at \( 3 \) (because the inequality includes equality, i.e., \( q = 3 \) is part of the solution) and draw a ray to the left (towards the smaller numbers) to represent all values of \( q \) that are less than or equal to \( 3 \).

Answer:

The solution of the inequality is \( q\leq3 \). On the number - line, there is a closed circle at \( 3 \) and a ray extending to the left.