First, group and combine like terms on each side of the inequality:
-w - 4w + 9 <= w - 21 - w−w−4w+9≤w−21−w
-1w - 4w + 9 <= w - w - 21−1w−4w+9≤w−w−21
(-1 - 4)w + 9 <= 0 - 21(−1−4)w+9≤0−21
-5w + 9 <= -21−5w+9≤−21
Next, subtract color(red)(9)9 from each side of the inequality to isolate the ww term while keeping the inequality balanced:
-5w + 9 - color(red)(9) <= -21 - color(red)(9)−5w+9−9≤−21−9
-5w + 0 <= -30−5w+0≤−30
-5w <= -30−5w≤−30
Now, divide each side of the inequality by color(blue)(-5)−5 to solve for ww while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we need to reverse the inequality operator:
(-5w)/color(blue)(-5) color(red)(>=) (-30)/color(blue)(-5)−5w−5≥−30−5
(color(red)(cancel(color(black)(-5)))w)/cancel(color(blue)(-5)) color(red)(>=) 6
w >= 6
