Simplify

$13.5-[5+0.5\times (9-3\times 2\left)\right]$

The correct option is 7.

To simplify the given mathematical expression, we follow the order of operations (PEMDAS/BODMAS rule). This rule dictates the sequence in which operations must be performed:
1. Parentheses/Brackets (innermost first)
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)

The given expression is:
$13.5-[5+0.5\times (9-3\times 2\left)\right]$

Step 1: Simplify the innermost parentheses $(9-3\times 2)$.
Within these parentheses, we perform multiplication before subtraction:
$3\times 2=6$
Now substitute this back:
$9-6=3$

Substituting this value back into the main expression gives:
$13.5-[5+0.5\times 3]$

Step 2: Simplify the expression inside the square brackets $[5+0.5\times 3]$.
We perform multiplication before addition:
$0.5\times 3=1.5$
Now perform the addition:
$5+1.5=6.5$

Substituting this value back into the main expression gives:
$13.5-6.5$

Step 3: Perform the final subtraction.
$13.5-6.5=7$

Thus, the simplified value of the expression is 7.