Solve the equation 2x + 13 * 18 + 6 * 4.4 = 405.

Step-by-step solution

1. 1

   Evaluate the numeric products first. None of them involve $x$, so multiplication is done before any rearranging — this is just order of operations applied to a constant:

   $13 \cdot 18 = 234, \qquad 6 \cdot 4.4 = 26.4$

2. 2

   Rewrite with a single constant.

   $2x + 234 + 26.4 = 405 \quad\Longrightarrow\quad 2x + 260.4 = 405$

   Combining the constants now means only one subtraction is needed later, which halves the chance of an arithmetic slip.

3. 3

   Isolate the x term.

   $2x = 405 - 260.4 = 144.6$

4. 4

   Divide by the coefficient.

   $x = \frac{144.6}{2} = 72.3$

5. 5

   Verify against the original expression. $2(72.3) = 144.6$, plus $234$ gives $378.6$, plus $26.4$ gives $405.0$ exactly. The decimal $.6$ and $.4$ combine to a whole number, which is a useful sign the arithmetic is right.