Final answer:
The equation 1 − x/2 = 1 has x = 0 as its solution. For more complex equations like quadratics, the quadratic formula is used to find the values of x, and negative solutions are disregarded for physical quantities.
Step-by-step explanation:
To solve the equation 1 − x/2 = 1, we can directly see that the term −x/2 must be equal to 0 for the equation to be true, since 1 − 0 equals 1. This leads us to x = 0.
Now, let's address the more complex equations provided in the examples. When we see an equation like (2x)² = 4.0(1 − x)², we need to take the square root of both sides to simplify it, giving us 2x(1 − x). This can be expanded and rearranged into a quadratic equation, which can then be solved for x. Similarly, for equations like x² + 1.2 x 10−2x −6.0 × 10−3 = 0, we would use the quadratic formula to find the values of x. It's essential to remember that when you have a quadratic equation of the form ax² + bx + c = 0, you can apply the quadratic formula.
Additionally, in situations where an approximation can be made (e.g., when x << 0.25), you can simplify the equation before solving it. However, for equations related to physical quantities like concentration, we disregard negative solutions as they are not physically viable, leaving us with the positive answer.