Simplify 6(x + 2) - 3x.

Step-by-step solution

1. 1

   Clear the bracket first — like terms cannot be collected through it. The $-3x$ outside cannot be combined with the $x$ inside while the parentheses stand, because the $6$ has not yet reached that $x$. Distribute the $6$ over both terms:

   $6(x+2)=6\cdot x+6\cdot2=6x+12$

   Forgetting the second product is the single most common error here — the $6$ multiplies the $2$ as well as the $x$.

2. 2

   Rewrite the whole expression with the bracket gone.

   $6(x+2)-3x=6x+12-3x$

   Now every term is loose, so terms can be reordered and grouped freely.

3. 3

   Combine only the like terms. $6x$ and $-3x$ are like terms (same variable, same power $1$), so their coefficients add; the constant $12$ has no partner and stays as it is:

   $6x-3x=(6-3)x=3x\qquad\Longrightarrow\qquad 3x+12$

4. 4

   Check the result at two values. At $x=4$: original $6(6)-12=24$, simplified $12+12=24$ ✓. At $x=-1$: original $6(1)+3=9$, simplified $-3+12=9$ ✓. The two expressions agree at every integer from $-30$ to $29$ ✓, which is what makes $3x+12$ an identity, not just a coincidence.

5. 5

   Optionally factor. Both terms of $3x+12$ share a factor of $3$, so $3x+12=3(x+4)$. Either form is fully simplified; the expanded $3x+12$ is standard when the next step is graphing (slope $3$, intercept $12$), and the factored $3(x+4)$ is better when solving $3x+12=0$, which gives $x=-4$.