Question

4.) 12(n - 8) = -120
5.) -2(n - 12) = 40
6.) 13 + \frac{n}{-4} = 5
7.) 6\left(n + \frac{2}{3}\
ight) = -20
8.) -3.2 = -5n - 0.7
9.) -11(2n - 2) = -11
10.) 0.4(n + 20) = 12.4
11.) 25 = 13 + \frac{n}{-6}
12.) 15\left(n - \frac{2}{5}\
ight) = -51

Explanation:

7. Step1: Divide both sides by 6

$n + \frac{2}{3} = \frac{-20}{6} = -\frac{10}{3}$

7. Step2: Subtract $\frac{2}{3}$ from both sides

$n = -\frac{10}{3} - \frac{2}{3} = -\frac{12}{3} = -4$

8. Step1: Add 0.7 to both sides

$-3.2 + 0.7 = -5n$
$-2.5 = -5n$

8. Step2: Divide both sides by -5

$n = \frac{-2.5}{-5} = 0.5$

9. Step1: Divide both sides by -11

$3n - 2 = \frac{-11}{-11} = 1$

9. Step2: Add 2 to both sides

$3n = 1 + 2 = 3$

9. Step3: Divide both sides by 3

$n = \frac{3}{3} = 1$

10. Step1: Divide both sides by 0.4

$n + 20 = \frac{12.4}{0.4} = 31$

10. Step2: Subtract 20 from both sides

$n = 31 - 20 = 11$

11. Step1: Subtract 13 from both sides

$25 - 13 = \frac{n}{-6}$
$12 = \frac{n}{-6}$

11. Step2: Multiply both sides by -6

$n = 12 \times (-6) = -72$

12. Step1: Divide both sides by 15

$n - \frac{2}{3} = \frac{-51}{15} = -\frac{17}{5}$

12. Step2: Add $\frac{2}{3}$ to both sides

$n = -\frac{17}{5} + \frac{2}{3} = \frac{-51 + 10}{15} = -\frac{41}{15} \approx -2.73$
(Matching the given options, $n=-2.7$ is the closest, exact value is $-\frac{41}{15}$)

Answer:

7.) $n=-4$ (orange)
8.) $n=0.5$ (blue)
9.) $n=1$ (green)
10.) $n=11$
11.) $n=-72$ (light blue)
12.) $n=-\frac{41}{15} \approx -2.7$ (dark blue)