|9х+15|=6

To solve the equation \(|9x + 15| = 6\), we will consider the two cases resulting from the absolute value. ### Case 1: \[ 9x + 15 = 6 \] Subtract 15 from both sides: \[ 9x = 6 - 15 \] \[ 9x = -9 \] Now divide by 9: \[ x = -1 \] ### Case 2: \[ 9x + 15 = -6 \] Subtract 15 from both sides: \[ 9x = -6 - 15 \] \[ 9x = -21 \] Now divide by 9: \[ x = -\frac{21}{9} = -\frac{7}{3} \] ### Solutions: The solutions to the equation \(|9x + 15| = 6\) are: \[ x = -1 \quad \text{and} \quad x = -\frac{7}{3} \]