Question

(+8)*(2x-3)<0

Answer 1

(x+2)(x^2+4-2x)(2x-3)<0
(x+2)((x-1)^2+3)(2x-3)<0
(x+2)(2x-3)<0

___>0____-2____<0____3/2____>0_____
(-2;3/2)

Answer 2

To solve the inequality $(8)(2x - 3) < 0$, you can follow these steps:

1. First, simplify the expression within the parentheses:

   $8 \cdot 2x = 16x$ $8 \cdot (-3) = -24$

   So, the inequality becomes:

   $16x - 24 < 0$

2. Add 24 to both sides of the inequality to isolate $16x$:

   $16x - 24 + 24 < 0 + 24$

   This simplifies to:

   $16x < 24$

3. Finally, divide both sides by 16 to solve for $x$:

   $\frac{16x}{16} < \frac{24}{16}$

   This simplifies to:

   $x < \frac{3}{2}$

So, the solution to the inequality $(8)(2x - 3) < 0$ is $x < \frac{3}{2}$.