What is the solution of (x+8)/(5x+-1)>0?

the solution set is (-infinity, -8) ∪ (-8, 1/5)

Step-by-step explanation:

x + 8 changes sign at x = -8.  

I'll assume you meant 5x - 1 (as 5x+- is meaningless).  5x - 1 changes sign at x = 1/5.

Subdivide the x-axis using the two x-values found above:

(negative infinity, -8), (-8, 1/5), (1/5, infinity.

Choose a representative value from each interval.  I'm choosing x = -10, x = 0 and x = 1.

Now test the given inequality at each of these x-values.  Is the result true or false?

 x + 8

> 0

5x - 1

For x = -10:

-10 + 8

> 0 => -2/(-51) => 2/51     This is TRUE

5(-10) - 1

For x = 1:

 1 + 8

> 0  =>  9/4     This is TRUE

  5 - 1

For x = 0:

     8

> 0    This is FALSE

    - 1

Therefore the solution set is (-infinity, -8) ∪ (-8, 1/5)

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

step-by-step explanation: