Let's simplify the given expressions step-by-step using the order of operations (PEMDAS/BODMAS).
### Expression 1: [tex]\( 4 + 6 - 7 \times 15 \div 3 \)[/tex]
1. Multiplication and Division (left to right):
[tex]\[
7 \times 15 = 105
\][/tex]
[tex]\[
105 \div 3 = 35
\][/tex]
2. Addition and Subtraction (left to right):
[tex]\[
4 + 6 = 10
\][/tex]
[tex]\[
10 - 35 = -25
\][/tex]
So, the simplified result of the first expression is:
[tex]\[
4 + 6 - 7 \times 15 \div 3 = -25.0
\][/tex]
### Expression 2: [tex]\( 44 - \{26 + (-84 \times 84 \div 42)\} \)[/tex]
1. Calculate inside the curly brackets:
a. Multiplication and Division (left to right):
[tex]\[
-84 \times 84 = -7056
\][/tex]
[tex]\[
-7056 \div 42 = -168
\][/tex]
b. Addition inside the braces:
[tex]\[
26 + (-168) = -142
\][/tex]
2. Subtraction outside the braces:
[tex]\[
44 - (-142) = 44 + 142 = 186
\][/tex]
So, the simplified result of the second expression is:
[tex]\[
44 - \{26 + (-84 \times 84 \div 42)\} = 186.0
\][/tex]
### Expression 3: [tex]\( 230 \times [184 - \{276 \div 138 \times 124 \div 4 - 30\}] \)[/tex]
1. Calculate inside the curly brackets:
a. Division and Multiplication (left to right):
[tex]\[
276 \div 138 = 2
\][/tex]
[tex]\[
2 \times 124 = 248
\][/tex]
[tex]\[
248 \div 4 = 62
\][/tex]
b. Subtraction inside the braces:
[tex]\[
62 - 30 = 32
\][/tex]
2. Subtraction inside the square brackets:
[tex]\[
184 - 32 = 152
\][/tex]
3. Finally, multiplication:
[tex]\[
230 \times 152 = 34960
\][/tex]
So, the simplified result of the third expression is:
[tex]\[
230 \times [184 - \{276 \div 138 \times 124 \div 4 - 30\}] = 34960.0
\][/tex]
### Summary
The simplified results for the given expressions are:
1. [tex]\( 4 + 6 - 7 \times 15 \div 3 = -25.0 \)[/tex]
2. [tex]\( 44 - \{26 + (-84 \times 84 \div 42)\} = 186.0 \)[/tex]
3. [tex]\( 230 \times [184 - \{276 \div 138 \times 124 \div 4 - 30\}] = 34960.0 \)[/tex]
