Solve 20x - 2 - (4x + 2) = 6 + 2x for x.

Step-by-step solution

1. 1

   Remove the bracket, negating both terms inside. A minus sign in front of a bracket flips the sign of everything within:

   $-(4x+2)=-4x-2\quad\Rightarrow\quad 20x-2-4x-2=6+2x$

   Writing $-4x+2$ instead is the standard slip and shifts the answer.

2. 2

   Combine like terms on the left.

   $20x-4x=16x,\qquad -2-2=-4\quad\Rightarrow\quad 16x-4=6+2x$

3. 3

   Gather the variable terms. Subtract $2x$ from both sides:

   $14x-4=6$

4. 4

   Gather the constants. Add $4$:

   $14x=10$

5. 5

   Divide and reduce.

   $x=\frac{10}{14}=\frac57\approx 0.7143$

   Always reduce: $10$ and $14$ share the factor $2$.

6. 6

   Check exactly. With $x=\frac57$: the left side is $\frac{100}{7}-2-\left(\frac{20}{7}+2\right)=\frac{80}{7}-4=\frac{52}{7}$, and the right side is $6+\frac{10}{7}=\frac{52}{7}$ ✓.