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

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:

$2 \times + 1 \times \left\{\frac{2 g + 3}{2}\right\} > 2 \times - 7$

this gives

$2 g + 3 \succ 14$

subtract -3 from both sides

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

$2 g > - 17$ divide both sides by 2 gives. s
$2 \frac{g}{2} > - \frac{17}{2}$

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

$2 \times - 1 \times \left\{\frac{2 g + 3}{2}\right\} > 2 \times - 7$

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

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

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

$- 2 \frac{g}{-} 2 > - \frac{11}{-} 2$ : $\frac{>}{-} = <$ 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