How do you solve and graph #abs((2g+3)/2)> -7#?

1 Answer
Aug 12, 2018

Solve the equation twice once for the positive value of the absolute value and once for the negative value of the absolute value and then graph the results.

Explanation:

# 2 xx +1 xx {( 2g +3)/2} > 2 xx -7#

this gives

# 2g +3 >-14 #

subtract -3 from both sides

# 2g + 3-3 > -14 -3 # so

# 2g > -17# divide both sides by 2 gives. s
# 2g/2 > -17/2 #

Draw an open circle at - 17/2 and a solid arrow going to the right.

# 2 xx -1 xx {( 2g +3) /2} > 2 xx -7 #

This give # -2g -3 > -14 #

Add +3 to both sides

# -2g -3 + 3 > -14 + 3 so

# -2g > -11 # divide both sides and the inequality by -1

# -2g/ -2 > -11/-2# : # >/(-) = <# so

# g < + 11/2

Draw an open circle at + 11/2 and a solid arrow going to the left.

the graph will be the line between - 17/2 and + 11/2