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

1 Answer
Aug 12, 2018

Answer:

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