Question

3/7w+1>9/7-4/5w

Answer 1

To solve the inequality, we need to isolate the variable 'w' on one side.

Let's start by getting rid of fractions by finding a common denominator. The common denominator of 7w and 5w is 35w.

Multiplying every term by 35w, we get:

3(35w/7) + 35w/5 > 9(35w/7) - 4(7w/5)

This simplifies to:

15w + 7(7w/5) > 45w - 28w/5

15w + 49w/5 > 45w - 28w/5

Now, let's combine like terms:

(75w + 49w) / 5 > (225w - 28w) / 5

(124w) / 5 > (197w) / 5

Now, we can cancel out the denominators:

124w > 197w

Next, we want to isolate the variable 'w' on one side. Subtracting 197w from both sides, we get:

124w - 197w > 0

-73w > 0

Finally, we divide both sides by -73, remembering to flip the inequality sign:

w < 0/-73

w < 0

Therefore, the solution to the inequality is w < 0.