What is the answer to |4n-15|=|n| ?

The answer to |4n-15|=|n| is n=3\lor n=5

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|4n-15|=|n|

∣ 4 n - 15 ∣ = ∣ n ∣

n = 3 or n = 5

Solution steps

∣ 4 n - 15 ∣ = ∣ n ∣

Find positive and negative intervals

n < 0, 0 \leq n < \frac{15}{4}, n \geq \frac{15}{4}

Solve the inequality for each interval

No Solution or n = 3 or n = 5

n = 3 or n = 5

\frac{x - 3}{5} = 3

3 ∣ 2 x ∣ - 9.75 = 2 \frac{1}{4}

5 ∣ 2 x + 3 ∣ + 4 x = 15

∣ 2 x ∣ = 4

∣ x - 2 ∣ = ∣ x + 2 ∣