Expand −76(3g+2).(1 point)

Question

Responses

−72g−73
negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction

72g−73
Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction

72g+2
Start Fraction 7 over 2 End Fraction g plus 2

−72g+2

Answer 1

To expand the expression \(-76(3g + 2)\), you'll need to distribute \(-76\) to both terms inside the parentheses:

1. Distributing to \(3g\): \[ -76 \cdot 3g = -228g \]

2. Distributing to \(2\): \[ -76 \cdot 2 = -152 \]

Now putting both results together, we have: \[ -228g - 152 \]

It appears the options listed in your question do not match this result. However, \(−228g−152\) is the correct expansion of the original expression.

Answer 2

Choose the closest one

Answer 3

Given the options you provided and the result we obtained from the expansion \(-76(3g + 2) = -228g - 152\), let's compare:

1. \(-72g−73\)
2. \(-\frac{7}{2}g - \frac{7}{3}\)
3. \(72g−73\)
4. \(\frac{7}{2}g - \frac{7}{3}\)
5. \(72g + 2\)
6. \(-72g + 2\)

The expansion yields \(-228g - 152\), and while none of the options match that exactly, the option \(-72g - 73\) is the one that is closest, considering the similar signs and structure, despite the numerical differences being relatively substantial (comparing coefficients of g and constants).

So, I would choose:

\(-72g−73\) as the closest option.