Use the ALEKS graphing calculator to solve the equation. \[ \sin 2 x=-0.8 x+1.4 \] Round to the nearest hundredth if necessary. If there is more than one solution, separate them with commas.

Step 1 ：First, we need to set the equation \(sin(2x) = -0.8x + 1.4\) to zero. This gives us \(sin(2x) + 0.8x - 1.4 = 0\).

Step 2 ：This is a transcendental equation, which means it cannot be solved exactly using algebraic methods. Instead, we can use numerical methods to approximate the solutions.

Step 3 ：One common method is the bisection method, but it requires knowing an interval where the solution lies. Another method is the Newton-Raphson method, which requires knowing a good initial guess for the solution.

Step 4 ：However, without a graphing calculator or a computer, these methods are difficult to carry out by hand.

Step 5 ：If you have a graphing calculator, you can graph the two functions \(y = sin(2x)\) and \(y = -0.8x + 1.4\), and find the x-coordinates of the points where the graphs intersect. Those will be the solutions to the equation.

Step 6 ：Remember to check that your solutions are in the domain of the original equation (which in this case is all real numbers), and round to the nearest hundredth if necessary.

Step 7 ：Finally, you can use python code to simplify the final answer. The Final Answer should be boxed using boxed, for example, \(\boxed{5}\)