How do you solve (4-2x)/(3x+4)<=0?

1 Answer
Jan 10, 2017

The answer is =x in ] -4/3,2]

Explanation:

Let f(x)=(4-2x)/(3x+4)

The domain of f(x) is D_f(x)=RR-{-4/3}

Now,

we construct a sign chart

color(white)(aaaa)xcolor(white)(aaaaa)-oocolor(white)(aaaa)-4/3color(white)(aaaaaa)2color(white)(aaaa)+oo

color(white)(aaaa)3+4xcolor(white)(aaaaa)-color(white)(aa)color(red)(∥)color(white)(aa)+color(white)(aaaa)+

color(white)(aaaa)4-2xcolor(white)(aaaaa)-color(white)(aa)color(red)(∥)color(white)(aa)-color(white)(aaaa)+

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

Therefore,

f(x)<=0, when x in ] -4/3,2]