Solve the inequality 3 <= - 6 - 5x < 12

Answer 1

To solve the inequality, we will break it down into two separate inequalities and solve each one individually.

For the left inequality, 3 ≤ -6 - 5x:
Starting with -6 - 5x, let's isolate the x on one side of the inequality:
-6 - 5x ≥ 3
Subtracting 6 from both sides, we get:
-5x ≥ 9
Dividing both sides by -5 and flipping the inequality sign, we get:
x ≤ -9/5

Now, for the right inequality, -6 - 5x < 12:
Starting with -6 - 5x, let's isolate the x on one side of the inequality:
-6 - 5x < 12
Subtracting 6 from both sides, we get:
-5x < 18
Dividing both sides by -5 and flipping the inequality sign, we get:
x > -18/5

Combining the two solutions, we have:

x ≤ -9/5 OR x > -18/5