Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 10, 2023

Solve the absolute value equation $|4n-15| = |n|$ . The solutions are $n = 3$ and $n = 5$ .

STEP 1

Question: What are the possible cases for the equation $|4n-15|=|n|$ ?
A) $4n-15=n$ and $4n-15=-n$ B) $4n-15=n$ and $4n+15=n$ C) $4n-15=n$ and $4n-15=n^2$ D) $4n-15=-n$ and $4n+15=n$
Answer: A) $4n-15=n$ and $4n-15=-n$

STEP 2

Question: Solve the equation $4n-15=n$ for $n$ .
A) $n=3$ B) $n=5$ C) $n=-3$ D) $n=-5$
Answer: B) $n=5$

STEP 3

Question: Does $n=5$ satisfy the condition $4n-15 \geq n$ and $n \geq 0$ ?
A) Yes B) No C) Cannot be determined D) The question is not valid
Answer: A) Yes

STEP 4

Question: Solve the equation $4n-15=-n$ for $n$ .
A) $n=3$ B) $n=5$ C) $n=-3$ D) $n=-5$
Answer: A) $n=3$

STEP 5

Question: Does $n=3$ satisfy the condition $4n-15 < n$ and $n < 0$ ?
A) Yes B) No C) Cannot be determined D) The question is not valid
Answer: B) No

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