How do you solve #9-g<4#?

2 Answers
Jul 3, 2015

Answer:

You may add or subtract equally on both sides.

Explanation:

In this case we subtract 9:
#->-g<-5#

We now want to get rid of the #-#-sign, which we can do by multiplying both sides by #-1#
But: when multiplying (both sides) by a negative number you have to reverse the sign of the inequality.

#->g>5#

Check your answer, and you can see it's OK.

Jul 3, 2015

Answer:

#g > 5#

Explanation:

Method 1
Given
#color(white)("XXXX")##9-g < 4#
Add #g# to both sides
#color(white)("XXXX")##9 < 4+g#
Subtract 4 from both sides
#color(white)("XXXX")##5 < g#
#color(white)("XXXX")##color(white)("XXXX")#which can be written as #g > 5#

Method 2
Given
#color(white)("XXXX")##9-g < 4#
Subteact #9# from both sides
#color(white)("XXXX")##-g < -5#
Multiply both sides by #(-1)# [but remember multiplication or division by a negative number requires that the orientation of the inequality be reversed]
#color(white)("XXXX")##g > 5#