Sure! Let's break down the expression step-by-step, and evaluate each component carefully.
The expression we need to evaluate is:
[tex]\[ 7 - \left[\frac{(-20 + 2)}{6} - (+4)\right] - \frac{(10 - 4)}{23} \][/tex]
Step 1: Start with the calculations inside the innermost parentheses.
[tex]\[
(-20 + 2) = -18
\][/tex]
Step 2: Next, divide [tex]\(-18\)[/tex] by [tex]\(6\)[/tex].
[tex]\[
\frac{-18}{6} = -3
\][/tex]
Step 3: Subtract [tex]\(+4\)[/tex] from [tex]\(-3\)[/tex].
[tex]\[
-3 - (+4) = -3 - 4 = -7
\][/tex]
So, the expression inside the brackets is:
[tex]\[
\left[\frac{(-20 + 2)}{6} - (+4)\right] = -7
\][/tex]
Step 4: Now, let’s rewrite the original expression with [tex]\(-7\)[/tex] substituted in place of the bracketed expression.
[tex]\[
7 - (-7) - \frac{(10 - 4)}{23}
\][/tex]
Step 5: Simplify the subtraction inside the remaining division.
[tex]\[
10 - 4 = 6
\][/tex]
So, the expression simplifies to:
[tex]\[
7 - (-7) - \frac{6}{23}
\][/tex]
Step 6: Subtracting a negative number is the same as adding the positive counterpart.
[tex]\[
7 - (-7) = 7 + 7 = 14
\][/tex]
So the expression is now:
[tex]\[
14 - \frac{6}{23}
\][/tex]
Step 7: Now, perform the division.
[tex]\[
\frac{6}{23} \approx 0.26086956521739130434782608695652
\][/tex]
Step 8: Finally, subtract this result from 14.
[tex]\[
14 - \frac{6}{23} \approx 14 - 0.26086956521739130434782608695652 = 13.739130434782608695652173913043
\][/tex]
Thus, the fully evaluated expression is approximately:
[tex]\[
13.73913043478261
\][/tex]
So, the result is:
[tex]\[
\boxed{13.73913043478261}
\][/tex]
