Question

Rewrite the equation 3+g2−8g+5g=56g+12 as two equations joined by “and.” Enter the smaller number first and use fractions if needed.(1 point) 3+g2−8g+5g=56g+12 and g≠

Answer 1

To rewrite the given equation \( 3 + g^2 - 8g + 5g = 56g + 12 \) as two equations joined by "and," we first simplify the left side:

1. Combine like terms:
\[
3 + g^2 - 8g + 5g = 3 + g^2 - 3g
\]
This simplifies to:
\[
g^2 - 3g + 3
\]

2. Set the equation equal to the right side:
\[
g^2 - 3g + 3 = 56g + 12
\]

3. Rearranging gives:
\[
g^2 - 3g - 56g + 3 - 12 = 0
\]
\[
g^2 - 59g - 9 = 0
\]

4. Then, we can state we have the equation and a constraint related to \( g \):
\[
g \neq \text{undefined value}
\]
However, since we need to determine a specific value to exclude (e.g., any values that would make the denominator zero), we need to consider if we had any divisions in the original equation.

In this case, it seems we don't have any divisions (hence no need for an exclusion), but let's express the result:

The two equations combined would be:

\[
g^2 - 59g - 9 = 0 \text{ and } g \neq \text{undefined value}
\]

As no specific exclusion arises from our calculation here, if "undefined" means we expect a particular case of \( g \), we recall that there's no denominator making any \( g \) undefined from our computations.

This gives us:
\[
g^2 - 59g - 9 = 0 \text{ and } g \text{ is a real number}
\]

If indeed there was a specific number we needed to avoid (like zero if it appeared in a denominator), we'd need to adjust that. Please clarify any specific constraint needed.