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

2 Answers
May 30, 2017

Answer:

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

Answer:

#omega>=6#

Explanation:

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