Question

1. \\(\frac{1}{8}n = 5\\)
2. \\(6a = -54\\)
3. \\(10 = -2k\\)
4. \\(2.7 = -0.9y\\)
5. \\(-23.4 = -13w\\)
6. \\(\frac{1}{15}z = 6\\)
7. you and three friends spend $35 on tickets at the movies. write and solve an equation to find the price \\(p\\) of one ticket.

Explanation:

Problem 14: Isolate n, multiply by 8

Multiply both sides by 8:
$8 \times \frac{1}{8}n = 5 \times 8$

Problem 15: Isolate a, divide by 6

Divide both sides by 6:
$\frac{6a}{6} = \frac{-54}{6}$

Problem 16: Isolate k, divide by -2

Divide both sides by -2:
$\frac{10}{-2} = \frac{-2k}{-2}$

Problem 17: Isolate y, divide by -0.9

Divide both sides by -0.9:
$\frac{2.7}{-0.9} = \frac{-0.9y}{-0.9}$

Problem 18: Isolate w, divide by -13

Divide both sides by -13:
$\frac{-23.4}{-13} = \frac{-13w}{-13}$

Problem 19: Isolate z, multiply by 15

Multiply both sides by 15:
$15 \times \frac{1}{15}z = 6 \times 15$

Problem 20: Step1: Set up ticket equation

Total people = 4, so:
$4p = 35$

Problem 20: Step2: Isolate p, divide by 4

Divide both sides by 4:
$\frac{4p}{4} = \frac{35}{4}$

Answer:

1. $n = 40$
2. $a = -9$
3. $k = -5$
4. $y = -3$
5. $w = 1.8$
6. $z = 90$
7. Equation: $4p=35$; $p = 8.75$ (or $\frac{35}{4}$)