How do you solve #-4w-13> -21# and graph the solution on a number line?

1 Answer
Aug 3, 2017

Answer:

See a solution process below:

Explanation:

First, add #color(red)(13)# to each side of the inequality to isolate the #w# term while keeping the inequality balanced:

#-4w - 13 + color(red)(13) > 21 + color(red)(13)#

#-4w - 0 > 34#

#-4w > 34#

Next, divide each side of the inequality by #color(blue)(-4)# to solve for #w# while keeping the inequality balanced. However, because we are multiplying or dividing the inequality by a negative number we must reverse the inequality operator:

#(-4w)/color(blue)(-4) color(red)(<) 34/color(blue)(-4)#

#(-color(red)(cancel(color(black)(4)))w)/cancel(color(blue)(-4)) color(red)(<) (17 xx 2)/color(blue)(2 xx -2)#

#w color(red)(<) (17 xx color(blue)(cancel(color(black)(2))))/color(blue)(color(black)(cancel(color(blue)(2))) xx -2)#

#w < -17/2#

To graph this we draw a dashed vertical line at #-17/2#. The line is dashed to indicate the inequality is a "less than" operator and does not include the value #-17/2#. Then you shade to the left of the line to indicated the "less than":

graph{x < -17/2 [-15, 5, -7.5, 7.5]}