Question

rewrite the equation 3+g/2-8g + 5g = 5/6g+12 as two equations joined by "and" enter the smaller number first and use fractions if needed.
3+g/2-8g +5g = 5/6g+12 and g ≠ (blank), (blank)

Answer 1

The given equation is:

\[ 3 + \frac{g}{2} - 8g + 5g = \frac{5}{6}g + 12. \]

First, we can simplify the equation:

1. Combine like terms on the left side:
\[
3 + \frac{g}{2} - 3g = \frac{5}{6}g + 12.
\]

2. This simplifies to:
\[
3 + \frac{g}{2} - \frac{18g}{6} = \frac{5}{6}g + 12,
\]
which can be further simplified to:
\[
3 - \frac{17g}{6} = 12.
\]

3. Isolate \(g\) on one side:
\[
-\frac{17g}{6} = 12 - 3,
\]
which gives:
\[
-\frac{17g}{6} = 9.
\]

4. Multiply both sides by -6/17:
\[
g = \frac{9 \cdot -6}{17},
\]
hence:
\[
g = -\frac{54}{17}.
\]

Now, we can express this as two equations. The smaller number is \(g = -\frac{54}{17}\) and we can assume a non-zero exclusion (since \(g\) cannot be equal to any value that makes the equation invalid; for instance, if we consider integer values).

Therefore, we can write it as:

\[ g = -\frac{54}{17} \text{ and } g \neq 0. \]