%2B(3)%2F(2x%2B1)%3D4-x-%3D-(1)%2F(2).jpeg "(2x+1)+(3)/(2x+1)=4 X =-(1)/(2)")
Solving the Equation: (2x+1) + (3)/(2x+1) = 4, where x = -1/2
This article explores the process of solving the given equation and analyzing the solution at x = -1/2.
The Equation:
We have the equation: (2x+1) + (3)/(2x+1) = 4
Substitution and Simplification:
Let's substitute x = -1/2 into the equation:
- (2(-1/2)+1) + (3)/(2(-1/2)+1) = 4
- (-1 + 1) + (3)/( -1 + 1) = 4
- 0 + (3)/0 = 4
The Problem: Division by Zero
We encounter a problem here: division by zero is undefined. This means that the equation is not solvable at x = -1/2.
Why does this happen?
The denominator (2x+1) becomes zero when x = -1/2. This creates a singularity in the equation, making it undefined at this specific point.
Conclusion:
The equation (2x+1) + (3)/(2x+1) = 4 has no solution at x = -1/2. This is due to the denominator becoming zero at that value, leading to undefined behavior in the equation.