To solve the inequality -3x - 1 ≥ 11, we will follow these steps:
Step 1: Add 1 to both sides of the inequality:
-3x - 1 + 1 ≥ 11 + 1
-3x ≥ 12
Step 2: Divide both sides of the inequality by -3 (since the coefficient of x is negative):
(-3x)/(-3) ≤ 12/(-3)
x ≤ -4
Therefore, the solution to the inequality is x ≤ -4.
To graph this inequality on a number line, we start by marking -4 as a closed circle (since the inequality includes equality) on the number line. Then, we shade the region to the left of -4, representing all the values of x that are less than or equal to -4.
Number line:
<-----------------------------●----------------------------->
-5 -4 -3 -2 -1 0
The shaded region:
<-----------------------------●----------------------------->
-5 -4 -3 -2 -1 0
Thus, the graph of the inequality -3x - 1 ≥ 11 is represented by a closed circle at -4 on the number line, and shading to the left of -4.