Question

What is the solution of |2x-1=1

Answer 1

Answer:

x = 1 and x = 0

Explanation:

The equation you provided is |2x - 1| = 1. To solve this equation, we can consider both the positive and negative cases for the absolute value.

Positive case: 2x - 1 = 1
Adding 1 to both sides:
2x = 2
Dividing both sides by 2:
x = 1

Negative case: -(2x - 1) = 1
Distributing the negative sign:
-2x + 1 = 1
Subtracting 1 from both sides:
-2x = 0
Dividing both sides by -2:
x = 0

Therefore, the equation |2x - 1| = 1 has two solutions: x = 1 and x = 0

Answer 2

x = 0 and x = 1.

Explanation:

To find the solution of the equation |2x - 1| = 1, we need to consider two cases, one for when the expression inside the absolute value is positive and one for when it is negative.

Case 1: (2x - 1) is positive:

When (2x - 1) is positive, the absolute value expression simplifies to:

2x - 1 = 1

Adding 1 to both sides of the equation:

2x = 2

Dividing both sides by 2:

x = 1

So, in this case, the solution is x = 1.

Case 2: (2x - 1) is negative:

When (2x - 1) is negative, the absolute value expression changes the sign, resulting in:

-(2x - 1) = 1

Expanding the negation:

-2x + 1 = 1

Subtracting 1 from both sides of the equation:

-2x = 0

Dividing both sides by -2:

x = 0

Therefore, in this case, the solution is x = 0.

In conclusion, the equation |2x - 1| = 1 has two solutions: x = 0 and x = 1.