6-2 one-step equations with rational coefficients practice and problem solving: a/b solve. 1. $\frac{1}{3}n = 4$ $n = \underline{\quad\quad}$ 2. $y + 0.4 = 2$ $y = \underline{\quad\quad}$ 3. $12 = 0.5a$ $a = \underline{\quad\quad}$ 4. $-1 = \frac{1}{3}v$ $v = \underline{\quad\quad}$ 5. $15.5z = -77.5$ $z = \underline{\quad\quad}$ 6. $\frac{t}{-11} = 11$ $t = \underline{\quad\quad}$ 7. $0.5m = 0.75$ $m = \underline{\quad\quad}$ 8. $\frac{r}{4} = 250$ $r = \underline{\quad\quad}$ write each sentence as an equation. 9. eight less than $\frac{1}{3}$ a number $n$ is $-13$. $\underline{\quad\quad}$ 10. a number $f$ multiplied by $-12.3$ is $-73.8$. $\underline{\quad\quad}$ write an equation. then, solve. 11. during unusually cold weather, the temperature in miami beach was $10{^\circ}c$. this was 12 degrees more than in tallahassee. what is the temperature in tallahassee? $\underline{\quad\quad}$ 12. a swimmer swam 48 kilometers in $d$ days. what is the value of $d$ if the swimmer swam an average of 3.2 kilometers daily? $\underline{\quad\quad}$ 13. fifteen tickets cost $193.75. what is the average cost of each ticket? $\underline{\quad\quad}$ 14. a student walks $\frac{1}{4}$ mile from her home to the store on her way to a friend’s house. if the store is $\frac{1}{3}$ of the way to her friend’s house, how far is her friend’s house from her home? $\underline{\quad\quad}$

Question

Accepted Answer

### Problem 1: $\boldsymbol{\frac{1}{3}n = 4}$
# Explanation:
## Step1: Multiply both sides by 3
To solve for $ n $, we multiply both sides of the equation $\frac{1}{3}n = 4$ by 3 to isolate $ n $.
$ 3\times\frac{1}{3}n = 4\times3 $
## Step2: Simplify both sides
Simplifying the left side, $ 3\times\frac{1}{3}n = n $, and the right side, $ 4\times3 = 12 $. So we get $ n = 12 $.
# Answer:
$ n = 12 $

### Problem 2: $\boldsymbol{y + 0.4 = 2}$
# Explanation:
## Step1: Subtract 0.4 from both sides
To solve for $ y $, we subtract 0.4 from both sides of the equation $ y + 0.4 = 2 $.
$ y + 0.4 - 0.4 = 2 - 0.4 $
## Step2: Simplify both sides
Simplifying the left side, $ y + 0.4 - 0.4 = y $, and the right side, $ 2 - 0.4 = 1.6 $. So we get $ y = 1.6 $.
# Answer:
$ y = 1.6 $

### Problem 3: $\boldsymbol{12 = 0.5a}$
# Explanation:
## Step1: Divide both sides by 0.5
To solve for $ a $, we divide both sides of the equation $ 12 = 0.5a $ by 0.5.
$ \frac{12}{0.5} = \frac{0.5a}{0.5} $
## Step2: Simplify both sides
Simplifying the left side, $ \frac{12}{0.5}=24 $, and the right side, $ \frac{0.5a}{0.5}=a $. So we get $ a = 24 $.
# Answer:
$ a = 24 $

### Problem 4: $\boldsymbol{-1 = \frac{1}{3}v}$
# Explanation:
## Step1: Multiply both sides by 3
To solve for $ v $, we multiply both sides of the equation $ -1 = \frac{1}{3}v $ by 3.
$ 3\times(-1)=3\times\frac{1}{3}v $
## Step2: Simplify both sides
Simplifying the left side, $ 3\times(-1)= - 3 $, and the right side, $ 3\times\frac{1}{3}v = v $. So we get $ v=-3 $.
# Answer:
$ v = - 3 $

### Problem 5: $\boldsymbol{15.5z=-77.5}$
# Explanation:
## Step1: Divide both sides by 15.5
To solve for $ z $, we divide both sides of the equation $ 15.5z=-77.5 $ by 15.5.
$ \frac{15.5z}{15.5}=\frac{-77.5}{15.5} $
## Step2: Simplify both sides
Simplifying the left side, $ \frac{15.5z}{15.5}=z $, and the right side, $ \frac{-77.5}{15.5}=-5 $. So we get $ z = - 5 $.
# Answer:
$ z = - 5 $

### Problem 6: $\boldsymbol{\frac{t}{-11}=11}$
# Explanation:
## Step1: Multiply both sides by - 11
To solve for $ t $, we multiply both sides of the equation $ \frac{t}{-11}=11 $ by - 11.
$ -11\times\frac{t}{-11}=11\times(-11) $
## Step2: Simplify both sides
Simplifying the left side, $ -11\times\frac{t}{-11}=t $, and the right side, $ 11\times(-11)=-121 $. So we get $ t=-121 $.
# Answer:
$ t = - 121 $

### Problem 7: $\boldsymbol{0.5m = 0.75}$
# Explanation:
## Step1: Divide both sides by 0.5
To solve for $ m $, we divide both sides of the equation $ 0.5m = 0.75 $ by 0.5.
$ \frac{0.5m}{0.5}=\frac{0.75}{0.5} $
## Step2: Simplify both sides
Simplifying the left side, $ \frac{0.5m}{0.5}=m $, and the right side, $ \frac{0.75}{0.5} = 1.5 $. So we get $ m = 1.5 $.
# Answer:
$ m = 1.5 $

### Problem 8: $\boldsymbol{\frac{r}{4}=250}$
# Explanation:
## Step1: Multiply both sides by 4
To solve for $ r $, we multiply both sides of the equation $ \frac{r}{4}=250 $ by 4.
$ 4\times\frac{r}{4}=250\times4 $
## Step2: Simplify both sides
Simplifying the left side, $ 4\times\frac{r}{4}=r $, and the right side, $ 250\times4 = 1000 $. So we get $ r = 1000 $.
# Answer:
$ r = 1000 $

### Problem 9: Eight less than $\boldsymbol{\frac{1}{3}}$ a number $n$ is - 13.
# Explanation:
"Eight less than $\frac{1}{3}$ a number $n$" means $\frac{1}{3}n-8$, and "is - 13" means this expression equals - 13. So the equation is $\frac{1}{3}n - 8=-13$.
# Answer:
$\frac{1}{3}n - 8=-13$

### Problem 10: A number $f$ multiplied by - 12.3 is - 73.8.
# Explanation:
"A number $f$ multiplied by - 12.3" is $-12.3f$, and "is - 73.8" means this expression equals - 73.8. So the equation is $-12.3f=-73.8$.
# Answer:
$-12.3f=-73.8$

### Problem 11: Temperature in Tallahassee
# Explanation:
## Step1: Define variable and write equation
Let $ x $ be the temperature in Tallahassee (in $^{\circ}\text{C}$). The temperature in Miami Beach ($10^{\circ}\text{C}$) is 12 degrees more than in Tallahassee, so the equation is $ x + 12=10 $.
## Step2: Solve for $ x $
Subtract 12 from both sides: $ x+12 - 12=10 - 12 $, which simplifies to $ x=-2 $.
# Answer:
The equation is $ x + 12 = 10 $ (where $ x $ is the temperature in Tallahassee), and the temperature in Tallahassee is $-2^{\circ}\text{C}$.

### Problem 12: Value of $d$
# Explanation:
## Step1: Define variable and write equation
The total distance is 48 kilometers, the average daily distance is 3.2 kilometers, and the number of days is $ d $. We know that distance = average daily distance×number of days, so the equation is $ 3.2d = 48 $.
## Step2: Solve for $ d $
Divide both sides by 3.2: $ \frac{3.2d}{3.2}=\frac{48}{3.2} $, which simplifies to $ d = 15 $.
# Answer:
The equation is $ 3.2d = 48 $, and $ d = 15 $.

### Problem 13: Average cost of each ticket
# Explanation:
## Step1: Define variable and write equation
Let $ c $ be the average cost of each ticket (in dollars). The cost of 15 tickets is $ 15c $, and it is equal to $ 193.75 $ dollars. So the equation is $ 15c=193.75 $.
## Step2: Solve for $ c $
Divide both sides by 15: $ c=\frac{193.75}{15}\approx12.92 $ (rounded to two decimal places).
# Answer:
The equation is $ 15c = 193.75 $, and the average cost of each ticket is approximately $ \$12.92 $.

### Problem 14: Distance to friend's house
# Explanation:
## Step1: Define variable and write equation
Let $ d $ be the distance from her home to her friend's house (in miles). The distance from her home to the store ($\frac{1}{4}$ mile) is $\frac{1}{3}$ of the way to her friend's house, so the equation is $\frac{1}{3}d=\frac{1}{4}$.
## Step2: Solve for $ d $
Multiply both sides by 3: $ d=\frac{1}{4}\times3=\frac{3}{4} $ mile.
# Answer:
The equation is $\frac{1}{3}d=\frac{1}{4}$, and the distance from her home to her friend's house is $\frac{3}{4}$ mile.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: $\boldsymbol{\frac{1}{3}n = 4}$

Step1: Multiply both sides by 3

Step2: Simplify both sides

Step1: Subtract 0.4 from both sides

Step2: Simplify both sides

Step1: Divide both sides by 0.5

Step2: Simplify both sides

Answer:

Problem 2: $\boldsymbol{y + 0.4 = 2}$