Question

Part A: Solve P = 2(l + w) for l. Show your work. Part B: Solve 4w − 7k = 28 for k. Show your work.

Answer 1

The equation given to us is called a literal equation. An equation made up of a whole bunch of different variables. If we need to isolate the l, we first have to get it out from inside that set of parenthesis. Do that by distributing the 2 in to get P = 2L + 2w. We will subtract 2w from both sides to get P - 2w = 2L, and then we have to divide everything by 2 to get L alone. That leaves us with

$\frac{P-2w}{2}=L$. That is also the same thing as

$\frac{1}{2}P-w=L$, whichever one you want. Now, solving 4w - 7k = 28 for k requires that we subtract 4w from both sides leaving us with -7k=28-4w. Now we divide everything by -7 and we end up with

$k=-4+\frac{4}{7}w$, which is also the same thing as

$k=\frac{4}{7}w-4$ if you don't like to start with a negative.