Simplify 9x - 14x + 6x.

Step-by-step solution

1. 1

   Confirm the terms really are alike. All three terms contain the same variable $x$ raised to the same power $1$. That is the precise condition for combining: only the coefficients interact, and the variable part is carried along untouched, exactly as $9$ apples $-\,14$ apples $+\,6$ apples stays in apples.

2. 2

   Factor the common $x$ out to make the arithmetic explicit.

   $9x-14x+6x=(9-14+6)x$

   This is the distributive property in reverse, and it is what licenses treating the problem as a pure number calculation.

3. 3

   Add the coefficients strictly left to right. Subtraction is not associative, so the order matters:

   $9-14=-5,\qquad-5+6=1$

   A common slip is computing $14-6=8$ first and reporting $9-8=1x$ by luck, or $-5$ by sign error. Left-to-right keeps it safe.

4. 4

   Write the simplified expression. The coefficient is $1$, and a coefficient of $1$ is conventionally left unwritten:

   $1x=x$

5. 5

   Check numerically. At $x=10$: $90-140+60=10$ ✓. At $x=-3$: $-27+42-18=-3$ ✓. The identity holds at every integer from $-20$ to $19$ ✓. Note the answer is $x$, not $0$ and not $1$ — the terms nearly cancel, leaving a single $x$ behind.