Solve the equation 1 x (1 - x) = 0.1.

Step-by-step solution

1. 1

   Apply the multiplicative identity. Multiplying any expression by $1$ leaves it unchanged, so the leading factor can simply be dropped:

   $1\times(1-x)=1-x\quad\Longrightarrow\quad 1-x=0.1$

   The bracket makes this look like a product that needs expanding into a quadratic; it is not. There is only one $x$ in the whole equation.

2. 2

   Isolate the term containing $x$. Subtract $1$ from both sides:

   $-x=0.1-1=-0.9$

3. 3

   Divide by $-1$. For an equation (unlike an inequality) multiplying by $-1$ needs no extra care:

   $x=0.9$

4. 4

   Check, and note the complement structure. $1-0.9=0.1$ $\checkmark$. Equations of the form $1-x=p$ appear constantly in probability, where $x$ and $p$ are complementary probabilities summing to $1$.