For this case we have the following equation:
[tex]\frac {5} {9} (g + 18) = \frac {1} {6} g + 3[/tex]
Applying distributive property on the left side of the equation we have:
[tex]\frac {5} {9} g + \frac {5 * 18} {9} = \frac {1} {6} g + 3\\\frac {5} {9} g + \frac {90} {9} = \frac {1} {6} g + 3\\\frac {5} {9} g + 10 = \frac {1} {6} g + 3[/tex]
Subtracting [tex]\frac {1} {6} g[/tex] to both sides of the equation:
[tex]\frac {5} {9} g- \frac {1} {6} + 10 = 3\\\frac {6 * 5-9 * 1} {9 * 6} g + 10 = 3\\\frac {30-9} {54} g + 10 = 3\\\frac {21} {54} g + 10 = 3\\\frac {7} {18} g + 10 = 3[/tex]
Subtracting 10 to both sides of the equation:
[tex]\frac {7} {18} g = 3-10\\\frac {7} {18} g = -7[/tex]
Multiplying by 18 on both sides:
[tex]7g = -7 * 18\\7g = -126[/tex]
Dividing between 7 on both sides:
[tex]g = \frac {-126} {7}\\g = -18[/tex]
Thus, the value of g is -18.
ANswer:
[tex]g = -18[/tex]
