independent practice
solve each equation. check your solution. (examples 1–3)
1. $6 = \frac{1}{12}v$
2. $-\frac{2}{3}w = 60$
3. $-\frac{7}{8}k = -21$
4. $9.6 = 1.2b$
5. $0.75a = -9$
6. $-413.4 = -15.9n$
7. $3\frac{1}{10}s = 6\frac{1}{5}$
8. $2\frac{2}{9} = -\frac{4}{5}m$
9. $-2\frac{4}{5} = -3\frac{1}{2}n$

Question

Accepted Answer

### Problem 1: $ 6 = \frac{1}{12}v $
# Explanation:
## Step1: Isolate $ v $ by multiplying both sides by 12.
$ 6 \times 12 = \frac{1}{12}v \times 12 $
## Step2: Simplify both sides.
$ 72 = v $
# Answer: $ v = 72 $

### Problem 2: $ -\frac{2}{3}w = 60 $
# Explanation:
## Step1: Isolate $ w $ by multiplying both sides by $ -\frac{3}{2} $.
$ -\frac{2}{3}w \times (-\frac{3}{2}) = 60 \times (-\frac{3}{2}) $
## Step2: Simplify both sides.
$ w = -90 $
# Answer: $ w = -90 $

### Problem 3: $ -\frac{7}{8}k = -21 $
# Explanation:
## Step1: Isolate $ k $ by multiplying both sides by $ -\frac{8}{7} $.
$ -\frac{7}{8}k \times (-\frac{8}{7}) = -21 \times (-\frac{8}{7}) $
## Step2: Simplify both sides.
$ k = 24 $
# Answer: $ k = 24 $

### Problem 4: $ 9.6 = 1.2b $
# Explanation:
## Step1: Isolate $ b $ by dividing both sides by 1.2.
$ \frac{9.6}{1.2} = \frac{1.2b}{1.2} $
## Step2: Simplify both sides.
$ 8 = b $
# Answer: $ b = 8 $

### Problem 5: $ 0.75a = -9 $
# Explanation:
## Step1: Isolate $ a $ by dividing both sides by 0.75.
$ \frac{0.75a}{0.75} = \frac{-9}{0.75} $
## Step2: Simplify both sides.
$ a = -12 $
# Answer: $ a = -12 $

### Problem 6: $ -413.4 = -15.9n $
# Explanation:
## Step1: Isolate $ n $ by dividing both sides by -15.9.
$ \frac{-413.4}{-15.9} = \frac{-15.9n}{-15.9} $
## Step2: Simplify both sides.
$ 26 = n $
# Answer: $ n = 26 $

### Problem 7: $ 3\frac{1}{10}s = 6\frac{1}{5} $
# Explanation:
## Step1: Convert mixed numbers to improper fractions. $ 3\frac{1}{10} = \frac{31}{10} $, $ 6\frac{1}{5} = \frac{31}{5} $
$ \frac{31}{10}s = \frac{31}{5} $
## Step2: Isolate $ s $ by multiplying both sides by $ \frac{10}{31} $.
$ \frac{31}{10}s \times \frac{10}{31} = \frac{31}{5} \times \frac{10}{31} $
## Step3: Simplify both sides.
$ s = 2 $
# Answer: $ s = 2 $

### Problem 8: $ 2\frac{2}{9} = -\frac{4}{5}m $
# Explanation:
## Step1: Convert mixed number to improper fraction. $ 2\frac{2}{9} = \frac{20}{9} $
$ \frac{20}{9} = -\frac{4}{5}m $
## Step2: Isolate $ m $ by multiplying both sides by $ -\frac{5}{4} $.
$ \frac{20}{9} \times (-\frac{5}{4}) = -\frac{4}{5}m \times (-\frac{5}{4}) $
## Step3: Simplify both sides.
$ -\frac{25}{9} = m $ or $ m = -2\frac{7}{9} $
# Answer: $ m = -\frac{25}{9} $ (or $ m = -2\frac{7}{9} $)

### Problem 9: $ -2\frac{4}{5} = -3\frac{1}{2}n $
# Explanation:
## Step1: Convert mixed numbers to improper fractions. $ -2\frac{4}{5} = -\frac{14}{5} $, $ -3\frac{1}{2} = -\frac{7}{2} $
$ -\frac{14}{5} = -\frac{7}{2}n $
## Step2: Isolate $ n $ by multiplying both sides by $ -\frac{2}{7} $.
$ -\frac{14}{5} \times (-\frac{2}{7}) = -\frac{7}{2}n \times (-\frac{2}{7}) $
## Step3: Simplify both sides.
$ \frac{4}{5} = n $
# Answer: $ n = \frac{4}{5} $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( 6 = \frac{1}{12}v \)

Step1: Isolate \( v \) by multiplying both sides by 12.

Step2: Simplify both sides.

Step1: Isolate \( w \) by multiplying both sides by \( -\frac{3}{2} \).

Step2: Simplify both sides.

Step1: Isolate \( k \) by multiplying both sides by \( -\frac{8}{7} \).

Step2: Simplify both sides.

Answer:

Problem 2: \( -\frac{2}{3}w = 60 \)