Question

5/9(g + 18) = 1/6g +3​

Answer 1

For this case we have the following equation:

$\frac {5} {9} (g + 18) = \frac {1} {6} g + 3$

Applying distributive property on the left side of the equation we have:

$\frac {5} {9} g + \frac {5 * 18} {9} = \frac {1} {6} g + 3\\\frac {5} {9} g + \frac {90} {9} = \frac {1} {6} g + 3\\\frac {5} {9} g + 10 = \frac {1} {6} g + 3$

Subtracting $\frac {1} {6} g$ to both sides of the equation:

$\frac {5} {9} g- \frac {1} {6} + 10 = 3\\\frac {6 * 5-9 * 1} {9 * 6} g + 10 = 3\\\frac {30-9} {54} g + 10 = 3\\\frac {21} {54} g + 10 = 3\\\frac {7} {18} g + 10 = 3$

Subtracting 10 to both sides of the equation:

$\frac {7} {18} g = 3-10\\\frac {7} {18} g = -7$

Multiplying by 18 on both sides:

$7g = -7 * 18\\7g = -126$

Dividing between 7 on both sides:

$g = \frac {-126} {7}\\g = -18$

Thus, the value of g is -18.

ANswer:

$g = -18$