Certainly! Let's break down the expression and solve it step by step:
Given:
[tex]\[ 2\left[\frac{(9-4)}{5}+\frac{(10-2)}{4}\right]+\frac{(9)(5)}{18}+2 \][/tex]
Step 1: Simplify the values inside the parentheses.
1. [tex]\((9 - 4)\)[/tex]
[tex]\[
9 - 4 = 5
\][/tex]
2. [tex]\((10 - 2)\)[/tex]
[tex]\[
10 - 2 = 8
\][/tex]
Step 2: Substitute these simplified values back into the expression and simplify the fractions.
1. [tex]\(\frac{(9-4)}{5} = \frac{5}{5} = 1.0\)[/tex]
2. [tex]\(\frac{(10-2)}{4} = \frac{8}{4} = 2.0\)[/tex]
Step 3: Add these fractions inside the brackets.
[tex]\[
\frac{(9-4)}{5} + \frac{(10-2)}{4} = 1.0 + 2.0 = 3.0
\][/tex]
Step 4: Multiply the result above by 2 (as indicated outside the first set of brackets).
[tex]\[
2 \times (1.0 + 2.0) = 2 \times 3.0 = 6.0
\][/tex]
Step 5: Evaluate the fraction inside the second set of square brackets.
[tex]\[
\frac{(9)(5)}{18} = \frac{45}{18} = 2.5
\][/tex]
Step 6: Combine all parts of the expression.
Add the results of the calculations:
[tex]\[
6.0 + 2.5 + 2
\][/tex]
Step 7: Add the values together to get the final result.
[tex]\[
6.0 + 2.5 + 2 = 10.5
\][/tex]
Thus, the final result of the given expression is:
[tex]\[
\boxed{10.5}
\][/tex]
