Question

What’s the answer to this problem |2x-4|-1>0?

a) x > 2

b) x < 2

c) x = 2

d) There is no solution for x.

Answer 1

To solve the inequality |2x-4|-1>0, consider two cases: when 2x-4 is positive and when 2x-4 is negative. The solution is x<2 or x>2.

Step-by-step explanation:

To solve the inequality |2x-4|-1>0, we need to consider two cases:

1. When 2x-4 is positive, we have |2x-4|-1=2x-4-1=2x-5>0.
2. When 2x-4 is negative, we have |2x-4|-1=-(2x-4)-1=-2x+4-1=-2x+3>0.

For case 1, we solve 2x-5>0:

2x-5>0
2x>5
x>5/2

For case 2, we solve -2x+3>0:

-2x+3>0
-2x>-3
x<3/2

Therefore, the solution to the inequality is x<3/2 or x>5/2, which can be written as x<2 or x>2.