Solve for x: 0 = 2145 - 30*11*4 + 6*11*4 + 5*11*4 + x*11*10.

Step-by-step solution

1. 1

   Evaluate every product before combining anything. Multiplication outranks addition, so each triple product is a single constant (or a single coefficient of $x$):

   $30\cdot 11\cdot 4=1320,\quad 6\cdot 11\cdot 4=264,\quad 5\cdot 11\cdot 4=220,\quad 11\cdot 10=110$

   Only the last one touches $x$, so the equation has exactly one variable term with coefficient $110$.

2. 2

   Rewrite with the numbers in place, keeping each sign attached.

   $0=2145-1320+264+220+110x$

   The minus belongs to the $1320$ term only; the two following products are added.

3. 3

   Combine the constants left to right.

   $2145-1320=825,\qquad 825+264=1089,\qquad 1089+220=1309$

   so the equation reduces to

   $0=1309+110x$

4. 4

   Isolate $x$. Subtract $1309$ and divide by $110$:

   $110x=-1309\ \Longrightarrow\ x=-\frac{1309}{110}$

   The fraction simplifies to a terminating decimal because $1309=11\cdot 119$ and $110=11\cdot 10$, so

   $x=-\frac{119}{10}=-11.9$

5. 5

   Check by substitution. With $x=-11.9$: $110\times(-11.9)=-1309$, and $1309+(-1309)=0$ ✓. The exact form $-\tfrac{119}{10}$ and the decimal $-11.9$ are the same number, so either is acceptable as the final answer.