Question

Solve and graph this inequality:

-3x-1\ge11

You will need to move your point below to earn full credit. 👇

Answer 1

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.