If |2x - 1 | > 3 , then which of the following could not be a value of x?
To determine which of the given values of x could not satisfy the inequality |2x - 1| > 3, we need to solve the inequality and find the range of x.
First, let's solve the inequality |2x - 1| > 3:
We have two cases to consider:
1. 2x - 1 > 3
2. -(2x - 1) > 3 (Note: We take the negative because we have the absolute value function)
1. Solving 2x - 1 > 3:
Add 1 to both sides: 2x > 4
Divide both sides by 2 (since we want to solve for x): x > 2
2. Solving -(2x - 1) > 3:
Distribute the negative sign: -2x + 1 > 3
Subtract 1 from both sides: -2x > 2
Divide both sides by -2 (since we have a negative coefficient): x < -1
So we have two separate inequalities:
1. x > 2
2. x < -1
Now, let's think about which values of x could not satisfy either of these conditions:
- If x > 2, any value of x greater than 2 would satisfy this condition.
- If x < -1, any value of x less than -1 would satisfy this condition.
Therefore, any value of x that is between -1 and 2, including -1 and 2 themselves, would not satisfy the inequality |2x - 1| > 3.
In summary, the values of x that could not be a solution to the inequality are the ones between -1 and 2, inclusive.