Question

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

Answer 1

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