Answer:
x = 1
Explanation:
To solve the given equation, we'll start by setting up the equation and simplifying it step by step:
The product of (x + 3) and (2x + 3) is 14 more than the product of (x + 1) and (2x + 1).
(x + 3)(2x + 3) = (x + 1)(2x + 1) + 14
Expanding both sides of the equation:
2x^2 + 3x + 6x + 9 = 2x^2 + x + 2x + 1 + 14
Combining like terms:
2x^2 + 9x + 9 = 2x^2 + 3x + 15
Subtracting (2x^2 + 3x + 15) from both sides:
2x^2 + 9x + 9 - 2x^2 - 3x - 15 = 0
Simplifying:
6x - 6 = 0
Adding 6 to both sides:
6x = 6
Dividing both sides by 6:
x = 1
Therefore, the value of x that satisfies the equation is x = 1.
Hope this helps!