\[ e^{1-3 x}=3-2 x \] Round to the nearest hundredth. If there is more than one solution, separate them with commas

To solve the equation \( e^{1-3x} = 3 - 2x \), we start by rewriting it to make it easier to analyze: 1. Take the natural logarithm of both sides to isolate the variable. However, in this case, it's more practical to work towards finding numerical solutions graphically or using numerical methods since it's not easy to isolate \( x \) algebraically. 2. Rearranging gives us \( e^{1-3x} - (3 - 2x) = 0 \). 3. Use a numerical method (like Newton's method or graphing the functions) to find where \( e^{1-3x} \) and \( 3 - 2x \) intersect. By graphing the two functions or using a numerical solver, we find the approximate solutions to this equation. The solutions are approximately \( x \approx 0.45 \) and \( x \approx 1.32 \). So, rounding to the nearest hundredth, the solutions are: \[ x \approx 0.45, 1.32 \]