Let's break down the given expression [tex]\(10 - \{3 \times 2) + 2 \times [2 - (9 \div 22)]\}=0\)[/tex] step by step.
### Step-by-Step Solution:
1. Evaluate the division inside the innermost brackets:
[tex]\[
\frac{9}{22} \approx 0.4091
\][/tex]
2. Evaluate the expression inside the square brackets next:
[tex]\[
2 - \frac{9}{22} \approx 2 - 0.4091 = 1.5909
\][/tex]
3. Evaluate the multiplication inside the square brackets:
[tex]\[
2 \times (2 - \frac{9}{22}) \approx 2 \times 1.5909 = 3.1818
\][/tex]
4. Evaluate the multiplication outside the curly-braces:
[tex]\[
3 \times 2 = 6
\][/tex]
5. Put it all together and evaluate the remaining expression:
[tex]\[
10 - 6 + 3.1818 = 4 + 3.1818 = 7.1818
\][/tex]
Now, let’s see if the final expression equals 0:
[tex]\[
10 - 6 + 3.1818 = 7.1818 \neq 0
\][/tex]
So, after evaluating each part step by step, we find that the expression equals approximately 7.1818, which is not equal to 0. The initial assertion that [tex]\(10-\{3 \times 2)+2 \times[2-(9 \div 22]\}=0\)[/tex] seems to be incorrect. The correct evaluation of the expression yields [tex]\(7.1818\)[/tex], not [tex]\(0\)[/tex].
