To determine which of the expressions have negative values, we need to evaluate each expression step-by-step and observe whether the result is negative. Let's go through each one:
1. Expression: [tex]\(2 + 2 \cdot (-3) \cdot 7\)[/tex]
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Let's break it down step-by-step:
[tex]\[
2 + 2 \cdot (-3) \cdot 7 = 2 + (2 \cdot -3) \cdot 7 = 2 + (-6) \cdot 7 = 2 + (-42) = 2 - 42 = -40
\][/tex]
Since [tex]\(-40\)[/tex] is negative, this expression has a negative value.
2. Expression: [tex]\(-2 \cdot \left(\frac{27}{9}\right) + 4\)[/tex]
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Let's break it down step-by-step:
[tex]\[
-2 \cdot \left(\frac{27}{9}\right) + 4 = -2 \cdot 3 + 4 = -6 + 4 = -2
\][/tex]
Since [tex]\(-2\)[/tex] is negative, this expression has a negative value.
3. Expression: [tex]\((14 + -2) \cdot (-6)\)[/tex]
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Let's break it down step-by-step:
[tex]\[
(14 + -2) \cdot (-6) = (14 - 2) \cdot (-6) = 12 \cdot (-6) = -72
\][/tex]
Since [tex]\(-72\)[/tex] is negative, this expression has a negative value.
4. Expression: [tex]\((4 - 10) - \left(\frac{8}{-2}\right)\)[/tex]
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Let's break it down step-by-step:
[tex]\[
(4 - 10) - \left(\frac{8}{-2}\right) = -6 - (-4) = -6 + 4 = -2
\][/tex]
Since [tex]\(-2\)[/tex] is negative, this expression has a negative value.
In summary, all four expressions have negative values:
- [tex]\(2 + 2(-3)(7)\)[/tex]
- [tex]\(-2(27 \div 9) + 4\)[/tex]
- [tex]\((14 + -2)(-6)\)[/tex]
- [tex]\((4 - 10) - (8 \div(-2))\)[/tex]
