### Instruction: Let \[g(x) = \left\{ \begin{aligned} 3x+6 & \quad \text{ if } x < 0 \\ 2x - 13 & \quad \text{ if } x \ge 0 \end{aligned} \right.\]Find all solutions to the equation $g(x) = 3.$.### Response: This is a piecewise function, so I need to consider two cases: when x is negative and when x is non-negative.
For the first case, I need to solve $3x + 6 = 3$, which means subtracting 6 from both sides and dividing by 3.
I get $x = -1$, which is a valid solution since it satisfies the condition $x < 0$.
For the second case, I need to solve $2x - 13 = 3$, which means adding 13 to both sides and dividing by 2.
I get $x = 8$, which is also a valid solution since it satisfies the condition $x \ge 0$.
Therefore, there are two solutions to the equation, and I can write them as an ordered pair or a set.