Question

Solve for
w
.
8/7 =10/w+4
Simplify your answer as much as possible.

Answer 1

Assuming the usual carelessness with parentheses, we have
8/7 =10/(w+4)
8(w+4) = 10*7
8w + 32 = 70
8w = 38
w = 19/4

Answer 2

To start, we'll isolate w on one side of the equation by subtracting 4 from both sides:

8/7 - 4 = 10/w

To combine the left side into a single fraction, we'll convert 4 to 28/7:

8/7 - 28/7 = 10/w

Simplifying the left side, we get:

-20/7 = 10/w

Multiplying both sides by w:

w(-20/7) = 10

Dividing both sides by -20/7:

w = -7/2

So the solution for w is -7/2 or -3.5.

Answer 3

This is another valid way to solve the equation. Multiplying both sides by (w+4) to isolate the variable was a good move. The resulting quadratic equation is:

8w + 32 = 10(w+4)
8w + 32 = 10w + 40
2w = 8
w = 4

However, it looks like there was a mistake when multiplying 10 and 7, which should give 70 instead of 100. This means that the correct calculation is:

8w + 32 = 70
8w = 38
w = 19/4

So the solution for w is 19/4 or 4.75.