Question

What is the solution of (3x+8)/(x-4) greater than or equal to=0

Answer 1

To solve the inequality (3x+8)/(x-4) ≥ 0, we need to find the values of x that satisfy this inequality. The solution is x ≤ 4 or x > 4.

Step-by-step explanation:

To solve the inequality (3x+8)/(x-4) ≥ 0, we need to find the values of x that satisfy this inequality. We can start by finding the critical points where the expression is equal to 0 or undefined. In this case, the expression is undefined when x = 4, so we have to exclude that value from our solution. Next, we can test some intervals to determine the sign of the expression in those intervals. For example, when x < 4, the expression is positive. Similarly, when x > 4, the expression is also positive. Therefore, the solution to the inequality is x ≤ 4 or x > 4.

Answer 2

`x\le \:-(8)/(3)`

`x>4`

Step-by-step explanation:

`(3x+8)/(x-4)\ge \:0`

Multiply both sides by (x - 4).

`(3x+8)/(x-4) (x-4) \ge \:0(x-4)`

`3x+8\leq \:0`

`3x+8-8\leq \:0-8`

`3x \leq \:-8`

`x\le \:-(8)/(3)`

Makes denominator equal to 0.

`x-4=0`

`x = 4`

`-8/3 \leq x<4` doesn't work in the original inequality.

`x>4` works in the original inequality.