Question

1. what is the first operation to perform when solving \\(\frac{b + c}{d}=e\\) for \\(b\\)?

a. multiply both sides by \\(d\\)
b. divide both sides by \\(e\\)
c. add \\(c\\) to both sides
d. subtract \\(c\\) from both sides

Explanation:

To solve \(\frac{b + c}{d}=e\) for \(b\), we use inverse operations. The expression \(b + c\) is divided by \(d\). To isolate the numerator \(b + c\), we first need to reverse the division by \(d\). The inverse of division is multiplication, so we multiply both sides by \(d\) first. This eliminates the denominator \(d\) on the left - hand side, giving \(b + c=e\times d\) (or \(b + c = ed\)), and then we can proceed to isolate \(b\) by subtracting \(c\) from both sides. Option b is incorrect because dividing by \(e\) does not help in isolating \(b\) or the numerator. Option c is incorrect as adding \(c\) would make the left - hand side more complicated. Option d is incorrect as we first need to eliminate the denominator before we can deal with the \(c\) term.

Answer:

a. Multiply both sides by \(d\)