Solve the equation 14x + 4 - (6x + 2) = 8x + 2.

Step-by-step solution

1. 1

   Distribute the minus sign across the whole bracket. The subtraction applies to both terms inside, not just the first:

   $14x + 4 - 6x - 2 = 8x + 2$

   Writing $-6x + 2$ here is the usual slip, and it would produce a spurious unique solution.

2. 2

   Combine like terms on the left.

   $(14x - 6x) + (4 - 2) = 8x + 2$

3. 3

   Compare the two sides.

   $8x + 2 = 8x + 2$

   The two sides are literally the same expression.

4. 4

   Interpret the result. Subtracting $8x + 2$ from both sides gives $0 = 0$, a statement true regardless of $x$. When the variable cancels and leaves a true statement, the equation is an identity: every real number satisfies it. (If it had left a false statement such as $0 = 5$, there would be no solutions at all.)

5. 5

   Spot-check two values. At $x = 0$: left $= 0 + 4 - 2 = 2$, right $= 2$. At $x = 7.5$: left $= 105 + 4 - 47 = 62$, right $= 60 + 2 = 62$. Both hold, as they must for every $x$.