[=absolute value
[-2x+1]>2
ok im doin inequalities and the only thing i don't get is if i take the absolute value off the -2x+1 goes to 2x+1 right?
<< the only thing i don't get is if i take the absolute value off the -2x+1 goes to 2x+1 right?>>
Wrong. |-2x + 1| becomes 2x-1 IF -2x +1 is less than zero.
To solve the inequality | -2x + 1 | > 2, you're correct that you can remove the absolute value symbol by considering two separate cases. Let's go through the process step-by-step:
1. Case 1: -2x + 1 > 2
In this case, we treat the expression -2x + 1 as positive:
-2x + 1 > 2
Subtract 1 from both sides:
-2x > 1
Divide both sides by -2, remembering to flip the inequality sign because we're dividing by a negative number:
x < -1/2
2. Case 2: -(-2x + 1) > 2
In this case, we treat the expression -2x + 1 as negative by introducing a negative sign.
-(-2x + 1) > 2
Simplify by distributing the negative sign:
2x - 1 > 2
Add 1 to both sides:
2x > 3
Divide both sides by 2:
x > 3/2
Therefore, the solution to the inequality | -2x + 1 | > 2 is x < -1/2 or x > 3/2.