First, subtract color(red)(5)5 from each segment of the system of inequalities to isolate the xx term while keeping the system balanced:
-15 - color(red)(5) <= -4x + 5 - color(red)(5) < -3 - color(red)(5)−15−5≤−4x+5−5<−3−5
-20 <= -4x + 0 < -8−20≤−4x+0<−8
-20 <= -4x < -8−20≤−4x<−8
Next, divide each segment by color(blue)(-4)−4 to solve for xx while keeping the system balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operators:
(-20)/color(blue)(-4) color(red)(>=) (-4x)/color(blue)(-4) color(red)(>) (-8)/color(blue)(-4)−20−4≥−4x−4>−8−4
5 color(red)(>=) (color(blue)(cancel(color(black)(-4)))x)/cancel(color(blue)(-4)) color(red)(>) 2
5 color(red)(>=) x color(red)(>) 2
Or
x <= 5; x > 2
Or, in interval notation:
(2, 5]
