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Solve the inequality |9 - 4n| < 5.

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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:

User Ronakg
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