How do you solve and write the following in interval notation: #20x + 28 <=4( 4x + 5) #?

1 Answer
Dec 8, 2017

Answer:

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

#20x + 28 <= color(red)(4)(4x + 5)#

#20x + 28 <= (color(red)(4) xx 4x) + (color(red)(4) xx 5)#

#20x + 28 <= 16x + 20#

Next, subtract #color(red)(28)# and #color(blue)(16x)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:

#20x - color(blue)(16x) + 28 - color(red)(28) <= 16x - color(blue)(16x) + 20 - color(red)(28)#

#(20 - color(blue)(16))x + 0 <= 0 - 8#

#4x <= -8#

Now, divide each side of the inequality by #color(red)(4)# to solve for #x# while keeping the inequality balanced:

#(4x)/color(red)(4) <= -8/color(red)(4)#

#(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) <= -2#

#x <= -2#

Or, in interval notation:

#(-oo, -2]#