How do you graph and solve #2-x<=3-(5x-4)#?

1 Answer
Jul 31, 2018

Answer:

#" "#
The given inequality

#color(red)(2-x<=3-(5x-4)#

can be simplified to

#color(blue)(x<=5/4#

Explanation:

#" "#
How do we graph and solve #color(red)(2-x<=3-(5x-4)# ?

We will try to simplify the inequality first before graphing:

#color(blue)(2-x<=3-(5x-4)#

Remove the parenthesis:

#rArr 2-x<= 3-5x+4#

Combining like terms and simplifying:

#rArr 2-x<= 7-5x#

Add #color(red)(5x# to both sides of the inequality:

#rArr 2-x+5x<= 7-5x+5x#

#rArr 2+4x<= 7-cancel (5x)+cancel (5x)#

Rearrange the terms and simplify:

#rArr 4x+2<=7#

Subtract #color(red)(2# from both sides of the inequality:

#rArr 4x+2-2<=7-2#

#rArr 4x+cancel 2-cancel 2<=7-2#

#rArr 4x<=5#

Divide both sides of the inequality by #color(red)(4#

#rArr 4x<=5#

#rArr (4x)/4<=5/4#

#rArr (cancel 4x)/cancel 4<=5/4#

#color(red)(x<=5/4#

This is our simplified inequality.

We can graph this inequality as shown below:

enter image source here

The solid line in the graph indicates the value #color(blue)([x=(5/4)]# that is part of the final solution.

Hope it helps.