Solve the equation 4x - 7 = 6x + 9.

Step-by-step solution

1. 1

   Decide which side keeps the variable. With $4x$ on the left and $6x$ on the right, subtracting the smaller coefficient $4x$ leaves a positive $2x$ and avoids a negative divisor later:

   $4x-7-4x=6x+9-4x\qquad\Longrightarrow\qquad-7=2x+9$

2. 2

   Move the constant away from the variable term. Subtract $9$ from both sides:

   $-7-9=2x\qquad\Longrightarrow\qquad-16=2x$

   Note $-7-9=-16$: two negatives accumulate, they do not cancel.

3. 3

   Divide by the coefficient of $x$.

   $x=\frac{-16}{2}=-8$

4. 4

   Verify in the original equation — both sides separately. Left: $4(-8)-7=-32-7=-39$. Right: $6(-8)+9=-48+9=-39$ ✓. Equal, so $x=-8$ is correct. Substituting into the rearranged form only would not catch an arithmetic slip made during rearranging, which is why the check goes back to the original.

5. 5

   Note the structure. Subtracting the two sides gives $(6x+9)-(4x-7)=2x+16$, which is zero exactly when $x=-8$ — a single crossing, as expected for two lines of different slope ($4$ versus $6$). Different slopes guarantee exactly one solution, in contrast to equal-slope equations that give either none or infinitely many.