Now we need to determine the sign of each factor in order to solve the inequality. We know that -8 is a negative number, so it won't affect the sign of the expression.
(3x - 1) will be positive when 3x - 1 > 0 3x > 1 x > 1/3
(2x + 3) will be positive when 2x + 3 > 0 2x > -3 x > -3/2
Therefore, the inequality holds when x is greater than 1/3 and less than -3/2:
-3/2 < x < 1/3
So, the values of x for which the expression is less than 0 are between -1.5 and 0.33.
To find the values of x for which the expression is less than 0, we can first expand the expression:
(-5-3)(1-3x)(-2x-3) = (-8)(1-3x)(-2x-3)
= 8(3x - 1)(2x + 3)
Now we need to determine the sign of each factor in order to solve the inequality. We know that -8 is a negative number, so it won't affect the sign of the expression.
(3x - 1) will be positive when 3x - 1 > 0
3x > 1
x > 1/3
(2x + 3) will be positive when 2x + 3 > 0
2x > -3
x > -3/2
Therefore, the inequality holds when x is greater than 1/3 and less than -3/2:
-3/2 < x < 1/3
So, the values of x for which the expression is less than 0 are between -1.5 and 0.33.