x/(x-3)<4
first: x-3>0 => x>3
x/(x-3)<4 => x <4x-12 => 12/3<x => 4<x
s=(4, +inf)
second: x-3<0 => x<3
x/(-(x-3))<4 => x>-4x+12 => -12>-5x => -12/-5<x => 12/5<x
s= (12/5, 3)
i dont know what im doing wrong, whats the answer please?
+130516 x(x -3) < 4 simplify the left and add 4 to both sides
x^2 -3x -4 < 0 factor
(x - 4)(x + 1) < 0
Now...the answer comes from either this interval (-1, 4) or from these two intervals (-∞, -1) and (4, ∞)
Let's test 0 on the interval (-1, 4) in the factored form..we have
(0 -4) ( 0 + 1) < 0
(-4)(1) < 0
-4 < 0 and that's true .....
So....the answer is x = (-1 , 4)
Here's a graph of x^2 -3x -4 which confirms that this function is less than 0 on ( -1, 4).....
https://www.desmos.com/calculator/eu8yycgutf
+130516 x(x -3) < 4 simplify the left and add 4 to both sides
x^2 -3x -4 < 0 factor
(x - 4)(x + 1) < 0
Now...the answer comes from either this interval (-1, 4) or from these two intervals (-∞, -1) and (4, ∞)
Let's test 0 on the interval (-1, 4) in the factored form..we have
(0 -4) ( 0 + 1) < 0
(-4)(1) < 0
-4 < 0 and that's true .....
So....the answer is x = (-1 , 4)
Here's a graph of x^2 -3x -4 which confirms that this function is less than 0 on ( -1, 4).....
https://www.desmos.com/calculator/eu8yycgutf
