(2x%2B5)%3D(2x%2B3)(x-4)%2B5.jpeg "(x+1)(2x+5)=(2x+3)(x-4)+5")
Solving the Equation: (x+1)(2x+5) = (2x+3)(x-4) + 5
This article will guide you through the steps of solving the equation (x+1)(2x+5) = (2x+3)(x-4) + 5.
Expanding the Equation
First, we need to expand both sides of the equation by multiplying out the brackets.
- Left-hand side: (x+1)(2x+5) = 2x² + 7x + 5
- Right-hand side: (2x+3)(x-4) + 5 = 2x² - 5x - 12 + 5 = 2x² - 5x - 7
Now the equation becomes: 2x² + 7x + 5 = 2x² - 5x - 7
Simplifying the Equation
Next, we need to simplify the equation by moving all the terms to one side.
Subtracting 2x² from both sides, we get: 7x + 5 = -5x - 7
Adding 5x to both sides: 12x + 5 = -7
Subtracting 5 from both sides: 12x = -12
Solving for x
Finally, to isolate x, we divide both sides by 12:
x = -12 / 12
Therefore, the solution to the equation (x+1)(2x+5) = (2x+3)(x-4) + 5 is x = -1.
Verification
To verify our answer, we can substitute x = -1 back into the original equation:
- Left-hand side: (-1 + 1)(2(-1) + 5) = 0 * 3 = 0
- Right-hand side: (2(-1) + 3)(-1 - 4) + 5 = 1 * -5 + 5 = 0
Since both sides of the equation are equal to 0, our solution x = -1 is correct.