Question

1/2x (2x-4)>_(x-2) пжжжжж​

Answer 1

1/2х(2х-4)>х-2

х²-2х>х-2

х²-3х+2>0

(х-1)(х-2)>0

х∈(-∞; 1)∪(2; +∞)

Answer 2

To solve the inequality (1/2x)(2x-4) > (x-2), you can follow these steps:

1. First, simplify both sides of the inequality:

   (1/2x)(2x-4) > (x-2)

   Now, distribute (1/2x) into (2x-4):

   (1/2)(2x-4) > (x-2)

   (2x - 4)/2 > (x - 2)

2. Simplify the left side:

   (2x - 4)/2 is the same as (1/2)(2x - 4), which simplifies to (x - 2).

   So, the inequality becomes:

   x - 2 > (x - 2)

3. Now, subtract x from both sides of the inequality to isolate the constant term on the right side:

   x - x - 2 > (x - x - 2)

   -2 > -2

4. At this point, we have -2 > -2, which is a true statement. This means that the inequality holds true for all values of x.

So, the solution to the inequality (1/2x)(2x-4) > (x-2) is:

All real numbers (x ∈ ℝ) satisfy the inequality.