First, subtract color(red)(11)11 from each segment of the system of inequalities to isolate the xx term while keeping the system balanced:
-5 - color(red)(11) >= -2x + 11 - color(red)(11) >= -9 - color(red)(11)−5−11≥−2x+11−11≥−9−11
-16 >= -2x + 0 >= -20−16≥−2x+0≥−20
-16 >= -2x >= -20−16≥−2x≥−20
Now, divide each segment by color(blue)(-2)−2 to solve for xx while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative numbers we must also reverse the inequality operators:
(-16)/color(blue)(-2) color(red)(<=) (-2x)/color(blue)(-2) color(red)(<=) (-20)/color(blue)(-2)−16−2≤−2x−2≤−20−2
8 color(red)(<=) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) 10
8 color(red)(<=) x color(red)(<=) 10
Or
x >= 8 and x <= 10
Or, in interval notation:
[8, 10]