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12.

Solve the equation. If there is no solution, select no solution.
4|n|-19=13

1 answer

To solve the equation \( 4|n| - 19 = 13 \), follow these steps:

  1. Add 19 to both sides: \[ 4|n| - 19 + 19 = 13 + 19 \] \[ 4|n| = 32 \]

  2. Divide both sides by 4: \[ |n| = \frac{32}{4} \] \[ |n| = 8 \]

  3. Solve for \( n \): The absolute value equation \( |n| = 8 \) gives us two equations: \[ n = 8 \quad \text{or} \quad n = -8 \]

Thus, the solutions are \( n = 8 \) and \( n = -8 \).