Solve the equation [(3x + 3)/2x] + 2x - 1 = -3

In this question we are trying to find all the possible solutions of the variable x that will satisfy the given equation. Firstly, we see there is a denominator on one of the terms so we multiply all the terms in the equation by this denominator so as to simplify it. Next we can multiply the brackets out and bring all the terms to one side, while paying careful attention to the changes in signs. Now we have a quadratic equation and the simplest way to solve this is break up the x term and find a common bracket. Once we have done this we can easily solve for x, getting the ansers -1 and -3/4. Below is a step by step example of the process.

[(3x + 3)/2x] + 2x - 1 = -3

(3x + 3) + (2x)(2x - 1) = (2x)(-3)

3x + 3 + 4x² - 2x = -6x

4x² + 7x + 3  = 0

4x² + 4x + 3x + 3 = 0

4x(x + 1) + 3(x + 1) = 0

(x + 1)(4x + 3) = 0

x = -1 or x = -3/4