To find the value of x that satisfies the inequality 4x < 12 < 16 < 8x, we will break it down into two parts for clarity.
First, let’s solve the inequality 4x < 12. To isolate x, divide both sides by 4:
x < 3
Next, solve the inequality 8x > 16. Again, isolate x by dividing both sides by 8:
x > 2
Now we have two inequalities:
- x < 3
- x > 2
This means that x must be between 2 and 3, not including the endpoints. Therefore, the solution set for x can be expressed as:
2 < x < 3
In conclusion, any value of x that lies between 2 and 3 will satisfy the original inequality.