To determine which of the given expressions has a negative value, let's evaluate each one step-by-step.
### Expression 1:
[tex]\[ 7 + 3(-4)(2) \][/tex]
First, solve the multiplication inside the parentheses:
[tex]\[ 3 \times (-4) = -12 \][/tex]
Next, multiply the result by 2:
[tex]\[ -12 \times 2 = -24 \][/tex]
Finally, add 7 to the product:
[tex]\[ 7 + (-24) = 7 - 24 = -17 \][/tex]
So, the value of the first expression is [tex]\(-17\)[/tex], which is negative.
### Expression 2:
[tex]\[ -2 \left[ 12 \div (-3) \right] \][/tex]
First, solve the division inside the brackets:
[tex]\[ 12 \div (-3) = -4 \][/tex]
Next, multiply the result by [tex]\(-2\)[/tex]:
[tex]\[ -2 \times (-4) = 8 \][/tex]
So, the value of the second expression is [tex]\(8\)[/tex], which is positive.
### Expression 3:
[tex]\[ (15 - 7) - (9 \div 3) \][/tex]
First, solve the operations inside the parentheses:
[tex]\[ 15 - 7 = 8 \][/tex]
[tex]\[ 9 \div 3 = 3 \][/tex]
Next, subtract the second result from the first:
[tex]\[ 8 - 3 = 5 \][/tex]
So, the value of the third expression is [tex]\(5\)[/tex], which is positive.
### Expression 4:
[tex]\[ -5 \left[ 7 + (-14) \right] - 30 \][/tex]
First, solve the addition inside the brackets:
[tex]\[ 7 + (-14) = 7 - 14 = -7 \][/tex]
Next, multiply the result by [tex]\(-5\)[/tex]:
[tex]\[ -5 \times (-7) = 35 \][/tex]
Finally, subtract 30 from the product:
[tex]\[ 35 - 30 = 5 \][/tex]
So, the value of the fourth expression is [tex]\(5\)[/tex], which is positive.
### Conclusion:
The only expression among the given ones that has a negative value is:
[tex]\[ 7 + 3(-4)(2) \][/tex]
With the value of [tex]\(-17\)[/tex]. Thus, this is the expression that has a negative value.
