what are the intervals to be conidered when finding the solutions in 4/6x-4 - 2/2x+2
please help. i am so lost and confused
To find the intervals in which the equation 4/6x - 4 - 2/2x + 2 equals zero, you need to solve the equation and then analyze the signs of each term.
Let's simplify the equation first:
4/6x - 4 - 2/2x + 2
First, find the common denominator, which is 6:
(4/6)x - 4 - (2/6)x + 2
Combine like terms:
(4/6 - 2/6)x - 4 + 2
Simplify further:
(2/6)x - 2
Now, let's set this equation equal to zero and solve for x:
(2/6)x - 2 = 0
Add 2 to both sides:
(2/6)x = 2
Multiply both sides by 6 to isolate x:
2x = 12
Divide both sides by 2:
x = 6
So, the solution to the equation is x = 6.
Now, let's analyze the signs of each term to find the intervals:
For (2/6)x, the sign will be positive when x > 0 and negative when x < 0.
For -2, the sign will always be negative.
Based on this analysis, we can conclude:
When x > 0, the equation is positive.
When x < 0, the equation is negative.
Therefore, the solution interval is x < 0.