Let's evaluate each expression step-by-step:
1. Expression 1: [tex]\(7 + 3(-4)(2)\)[/tex]
- First, simplify inside the nested parentheses:
[tex]\[
-4 \cdot 2 = -8
\][/tex]
- Then, evaluate the multiplication:
[tex]\[
3 \cdot -8 = -24
\][/tex]
- Finally, add 7:
[tex]\[
7 + (-24) = 7 - 24 = -17
\][/tex]
So, the value of expression 1 is [tex]\(-17\)[/tex].
2. Expression 2: [tex]\(-2[12 \div (-3)]\)[/tex]
- First, perform the division inside the brackets:
[tex]\[
12 \div (-3) = -4
\][/tex]
- Then, multiply by [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot -4 = 8
\][/tex]
So, the value of expression 2 is [tex]\(8\)[/tex].
3. Expression 3: [tex]\((15 - 7) - (9 \div 3)\)[/tex]
- First, evaluate the subtraction inside the first parentheses:
[tex]\[
15 - 7 = 8
\][/tex]
- Then, perform the division inside the second parentheses:
[tex]\[
9 \div 3 = 3
\][/tex]
- Finally, subtract the results:
[tex]\[
8 - 3 = 5
\][/tex]
So, the value of expression 3 is [tex]\(5\)[/tex].
4. Expression 4: [tex]\(-5[7 + (-14)] - 30\)[/tex]
- First, simplify inside the bracket:
[tex]\[
7 + (-14) = 7 - 14 = -7
\][/tex]
- Then, multiply by [tex]\(-5\)[/tex]:
[tex]\[
-5 \cdot -7 = 35
\][/tex]
- Finally, subtract 30:
[tex]\[
35 - 30 = 5
\][/tex]
So, the value of expression 4 is [tex]\(5\)[/tex].
Comparing the values:
- Expression 1: [tex]\(-17\)[/tex]
- Expression 2: [tex]\(8\)[/tex]
- Expression 3: [tex]\(5\)[/tex]
- Expression 4: [tex]\(5\)[/tex]
The expression with a negative value is [tex]\(7 + 3(-4)(2)\)[/tex] with the value of [tex]\(-17\)[/tex].
