|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: \[ x = -1 \quad \text{and} \quad x = -\frac{7}{3} \]