Question

How do you solve `\frac { 3x + 7} { 14- 7x } \geq 0`?

Answer 1

The answer is `=x in [-7/3, 2[`

Explanation:

Let `f(x)=(3x+7)/(14-7x)`

The domain of `f(x)` is #D_f(x)=RR-{2}

Let's do the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-7/3` `color(white)(aaaa)` `2` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `(3x+7)` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `(14-7x)` `color(white)(aaa)` `+` `color(white)(aaaa)` `+` `∥` `color(white)(aa)` `-`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaaa)` `-` `color(white)(aaaa)` `+` `∥` `color(white)(aa)` `-`

Therefore,`f(x)>=0`, when `x in [-7/3, 2[`

graph{(3x+7)/(14-7x) [-11.34, 11.17, -5.03, 6.22]}