Answer:
To solve the inequality |9 - 4n| < 5, you need to consider two cases: one for when the expression inside the absolute value is positive and one for when it's negative. Here's how you can solve it step by step:
Case 1: When 9 - 4n is positive:
Set up the inequality without the absolute value:
9 - 4n < 5
Subtract 9 from both sides of the inequality:
-4n < 5 - 9
-4n < -4
Divide both sides by -4. Remember that when you divide by a negative number, you need to reverse the inequality sign:
n > -4 / -4
n > 1
Case 2: When 9 - 4n is negative:
Set up the inequality without the absolute value, but negate the expression inside:
-(9 - 4n) < 5
Distribute the negative sign on the left side:
-9 + 4n < 5
Add 9 to both sides of the inequality:
4n < 5 + 9
4n < 14
Divide both sides by 4:
n < 14 / 4
n < 3.5
So, there are two solutions for this inequality:
When n > 1 (from Case 1).
When n < 3.5 (from Case 2).
You can combine these solutions as follows:
1 < n < 3.5
This is the solution to the inequality |9 - 4n| < 5.
Explanation: