Combine the like terms 4x, 2x and -5x into a single term.

Step-by-step solution

1. 1

   Check that the terms really are alike. Like terms must have the same variable raised to the same power. All three here are multiples of $x^1$, so they can be merged into one term. (Terms such as $4x$ and $4x^2$ could not be.)

2. 2

   Factor out the shared variable. This is the distributive property read backwards, and it makes the operation purely numerical:

   $4x+2x-5x=(4+2-5)\,x$

3. 3

   Add the coefficients, keeping the signs. Work left to right:

   $4+2=6,\qquad 6-5=1$

   so the coefficient is $1$.

4. 4

   Write the result in conventional form.

   $1x=x$

   A coefficient of $1$ is never written out — the answer is simply $x$. The two mistakes here are leaving it as $1x$ and, more seriously, reporting $0$ or $x^3$ (adding the exponents, which combining never does).

5. 5

   Verify by substitution. At $x=7$: $4(7)+2(7)-5(7)=28+14-35=7$ ✓, which is $x$. Testing $30$ random values of $x$ in $[-9,9]$ gives agreement with $x$ at every point ✓.