Let's evaluate each expression step-by-step to determine which ones have negative values.
1. Evaluate [tex]\(2 + 2(-3)(7)\)[/tex]:
First, calculate inside the parentheses:
[tex]\[
-3 \times 7 = -21
\][/tex]
Then, multiply by 2:
[tex]\[
2 \times -21 = -42
\][/tex]
Finally, add 2:
[tex]\[
2 + (-42) = -40
\][/tex]
So, the value of [tex]\(2 + 2(-3)(7)\)[/tex] is [tex]\(-40\)[/tex], which is negative.
2. Evaluate [tex]\(-2(27 \div 9) + 4\)[/tex]:
First, perform the division inside the parentheses:
[tex]\[
27 \div 9 = 3
\][/tex]
Then, multiply by -2:
[tex]\[
-2 \times 3 = -6
\][/tex]
Finally, add 4:
[tex]\[
-6 + 4 = -2
\][/tex]
So, the value of [tex]\(-2(27 \div 9) + 4\)[/tex] is [tex]\(-2\)[/tex], which is negative.
3. Evaluate [tex]\((14 \div -2)(-6)\)[/tex]:
First, perform the division inside the parentheses:
[tex]\[
14 \div -2 = -7
\][/tex]
Then, multiply by -6:
[tex]\[
-7 \times -6 = 42
\][/tex]
So, the value of [tex]\((14 \div -2)(-6)\)[/tex] is [tex]\(42\)[/tex], which is positive.
4. Evaluate [tex]\((4 - 10) - (8 \div -2)\)[/tex]:
First, perform the subtraction and division inside the parentheses:
[tex]\[
4 - 10 = -6
\][/tex]
and
[tex]\[
8 \div -2 = -4
\][/tex]
Then, subtract -4 from -6:
[tex]\[
-6 - (-4) = -6 + 4 = -2
\][/tex]
So, the value of [tex]\((4 - 10) - (8 \div -2)\)[/tex] is [tex]\(-2\)[/tex], which is negative.
Summarizing the expressions:
- [tex]\(2 + 2(-3)(7) = -40\)[/tex] (negative)
- [tex]\(-2(27 \div 9) + 4 = -2\)[/tex] (negative)
- [tex]\((14 \div -2)(-6) = 42\)[/tex] (positive)
- [tex]\((4 - 10) - (8 \div -2) = -2\)[/tex] (negative)
Therefore, the expressions that have negative values are:
[tex]\[
2 + 2(-3)(7), \quad -2(27 \div 9) + 4, \quad \text{and} \quad (4 - 10) - (8 \div -2)
\][/tex]
