Question

Solve and graph this inequality:



`-3x-1\ge11`

Answer 1

To solve the inequality `-3x - 1 ≥ 11`, we will isolate the variable `x`.

Adding 1 to both sides of the inequality, we get

-3x - 1 + 1 ≥ 11 + 1

-3x ≥ 12

Next, divide both sides of the inequality by -3. Since we are dividing by a negative number, we need to flip the inequality sign.

(-3x)/(-3) ≤ 12/(-3)

x ≤ -4

Now, let's graph the solution.

First, draw a number line.

----*----*----*---

Next, mark the point -4 on the number line.

----*----*----*---
-4

Since x is less than or equal to -4, we shade the line to the left of -4.

<====*----*----*---

This represents the graph of the inequality `-3x - 1 ≥ 11`.