First, subtract color(red)(3) from each segment of the system of inequalities to isolate the x term while keeping the system balanced:
-color(red)(3) - 3 <= -color(red)(3) + 3 - 2x < -color(red)(3) + 11
-6 <= 0 - 2x < 8
-6 <= -2x < 8
Now, divide each segment by color(blue)(-2) to solve for x while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:
(-6)/color(blue)(-2) color(red)(>=) (-2x)/color(blue)(-2) color(red)(>) 8/color(blue)(-2)
3 color(red)(>=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>) -4
3 color(red)(>=) x color(red)(>) -4
Or
x > -4 and x <= 3
Or, in interval notation:
(-4, 3]
