How do you solve the inequality -w - 4w + 9 ≤ w - 21 - w?

2 Answers
May 30, 2017

See a solution process below:

Explanation:

First, group and combine like terms on each side of the inequality:

-w - 4w + 9 <= w - 21 - w

-1w - 4w + 9 <= w - w - 21

(-1 - 4)w + 9 <= 0 - 21

-5w + 9 <= -21

Next, subtract color(red)(9) from each side of the inequality to isolate the w term while keeping the inequality balanced:

-5w + 9 - color(red)(9) <= -21 - color(red)(9)

-5w + 0 <= -30

-5w <= -30

Now, divide each side of the inequality by color(blue)(-5) to solve for w 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)

(color(red)(cancel(color(black)(-5)))w)/cancel(color(blue)(-5)) color(red)(>=) 6

w >= 6

May 30, 2017

omega>=6

Explanation:

-omega-4omega+9<=omega-21-omegararr-5omega+9<=cancel(omega)-21-cancel(omega)rarr-5omega<=-30rarr5omega>=30rarromega>=30/5=6