Question

Which equation is equivalent to b=4c+7d
?


d=b+4c7


d=b−4c7


d=b−7c4


d=b+7c4

Answer 1

To find an equation equivalent to \( b = 4c + 7d \), we can solve for \( d \):

Starting with:
\[
b = 4c + 7d
\]

We can isolate \( d \) on one side of the equation:

1. Subtract \( 4c \) from both sides:
\[
b - 4c = 7d
\]

2. Now, divide both sides by 7 to solve for \( d \):
\[
d = \frac{b - 4c}{7}
\]

This can also be rewritten to match the form of the options given. Simplifying gives:
\[
d = \frac{b}{7} - \frac{4c}{7}
\]

Now let's compare with the given options. We need to recognize the alternative forms. However, the right form here should express \( d \) as a function of \( b \) and \( c \).

Among the given options:
- \( d = b - 4c7 \) is incorrect.
- \( d = b - 4c7 \) is essentially the same incorrect representation as above and likely contains a typographical error.
- \( d = b - 7c4 \) is incorrect.
- \( d = b + 7c4 \) is incorrect.

None of the provided options appear to correctly represent \( d \) from the derived equivalent equation \( d = \frac{b - 4c}{7} \).

If we were asked for an equivalent expression for \( b \) rearranged from the original equation, none of the provided equations seem to match.

If you have any more questions or need further assistance, feel free to ask!