How do you solve 9-g<4?

Jul 3, 2015

You may add or subtract equally on both sides.

Explanation:

In this case we subtract 9:
$\to - g < - 5$

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.

$\to g > 5$

Jul 3, 2015

$g > 5$

Explanation:

Method 1
Given
$\textcolor{w h i t e}{\text{XXXX}}$$9 - g < 4$
Add $g$ to both sides
$\textcolor{w h i t e}{\text{XXXX}}$$9 < 4 + g$
Subtract 4 from both sides
$\textcolor{w h i t e}{\text{XXXX}}$$5 < g$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$which can be written as $g > 5$

Method 2
Given
$\textcolor{w h i t e}{\text{XXXX}}$$9 - g < 4$
Subteact $9$ from both sides
$\textcolor{w h i t e}{\text{XXXX}}$$- g < - 5$
Multiply both sides by $\left(- 1\right)$ [but remember multiplication or division by a negative number requires that the orientation of the inequality be reversed]
$\textcolor{w h i t e}{\text{XXXX}}$$g > 5$