How do you solve and graph #(3 ( x - 5 )) / 4 > x + 1#?

1 Answer
Stefan V.
Aug 28, 2015

#x < -19#

Explanation:

Your goal here is to isolate #x# on one side of the inequality.

First, multiply the right-hand side of the inequality by #1= 4/4#

#(3(x-5))/4 > (x+1) * 4/4#

This is equivalent to

#3(x-5) > 4(x+1)#

Use the distributive property of multiplication to break up those parantheses

#3 * x - 3 * 5 > 4 * x + 4 * 1#

#3x - 15> 4x + 4#

This is equivalent to

#3x - 4x > 4 + 15#

#-x > 19#

Finally, multiply both sides by #(-1)# - don't forget to change the sign of the inequality!

#x < -19#

To graph this inequality, draw a dotted vertical line thorugh #x = -19# and shade the area to the left of the line, since you need values of #x# that are smaller than #-19#.

graph{x < -19 [-58.5, 58.54, -29.26, 29.3]}

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