Solve the equation 5 - 2(x - 1) = 1.

Step-by-step solution

1. 1

   Distribute $-2$ across the bracket. The multiplier carries the minus sign, so both inner terms flip:

   $-2(x-1)=-2x+2$

   Writing $-2x-2$ is the standard mistake; $-2\times(-1)=+2$.

2. 2

   Rewrite and combine the constants.

   $5-2x+2=1\quad\Longrightarrow\quad 7-2x=1$

3. 3

   Isolate the variable term. Subtract $7$ from both sides:

   $-2x=1-7=-6$

4. 4

   Divide by $-2$. A negative divided by a negative is positive:

   $x=\frac{-6}{-2}=3$

5. 5

   Check in the original form. $5-2(3-1)=5-2(2)=5-4=1$ $\checkmark$. Substituting into the original equation (not the expanded one) also confirms the distribution was done correctly.