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

Question

Kennedy Adams · Accepted Answer

See a solution process below:

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#

Avery Alexander · Answer

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

Abigail Allen · Answer

undefined First, simplify both sides of the inequality:

$-w - 4w + 9 \leq w - 21 - w$

Combine like terms:

$-5w + 9 \leq -21$

Subtract 9 from both sides:

$-5w \leq -30$

Divide both sides by -5 (note that dividing by a negative number reverses the inequality):

$w \geq 6$

So, the solution to the inequality is $w \geq 6$.