solve the equation. check your solution.
1. $\frac{4}{3} = \frac{2}{15}j$
2. $-23.6 = 5.9t$
3. $6 = -2r$
4. the area of a rectangle is 55.8 square inches. the width of the rectangle is 4.5 inches. write and solve an equation to find the length of the rectangle.
solve the equation. check your solution.
5. $\frac{x}{-6} = -4$
6. $-1.4x = 7$
7. $\frac{8}{3} = \frac{2}{15}j$
8. $10 = -2r$
show all your work below, including your checks:

Question

Accepted Answer

### 1. Solve $\boldsymbol{\frac{4}{3}=\frac{2}{15}j}$
# Explanation:
## Step1: Isolate $ j $ by multiplying both sides by $ \frac{15}{2} $
To solve for $ j $, we can multiply both sides of the equation by the reciprocal of $ \frac{2}{15} $, which is $ \frac{15}{2} $. This will cancel out the coefficient of $ j $ on the right - hand side.
$$
\frac{4}{3}\times\frac{15}{2}=j
$$
## Step2: Simplify the left - hand side
First, simplify the fraction multiplication. $ \frac{4\times15}{3\times2}=\frac{60}{6} = 10 $
## Check:
Substitute $ j = 10 $ back into the original equation:
Left - hand side: $ \frac{4}{3} $
Right - hand side: $ \frac{2}{15}\times10=\frac{20}{15}=\frac{4}{3} $
Since the left - hand side equals the right - hand side, the solution is correct.
# Answer:
$ j = 10 $

### 2. Solve $\boldsymbol{-23.6 = 5.9t}$
# Explanation:
## Step1: Isolate $ t $ by dividing both sides by $ 5.9 $
To solve for $ t $, we divide both sides of the equation by $ 5.9 $.
$$
t=\frac{-23.6}{5.9}
$$
## Step2: Simplify the division
$ \frac{-23.6}{5.9}=- 4 $
## Check:
Substitute $ t=-4 $ back into the original equation:
Right - hand side: $ 5.9\times(-4)=-23.6 $
Since the left - hand side ($ - 23.6 $) equals the right - hand side, the solution is correct.
# Answer:
$ t=-4 $

### 3. Solve $\boldsymbol{6=-2r}$
# Explanation:
## Step1: Isolate $ r $ by dividing both sides by $ - 2 $
To solve for $ r $, we divide both sides of the equation by $ -2 $.
$$
r=\frac{6}{-2}
$$
## Step2: Simplify the division
$ \frac{6}{-2}=-3 $
## Check:
Substitute $ r = - 3 $ back into the original equation:
Right - hand side: $ -2\times(-3)=6 $
Since the left - hand side ($ 6 $) equals the right - hand side, the solution is correct.
# Answer:
$ r=-3 $

### 4. Find the length of the rectangle
# Explanation:
## Step1: Recall the formula for the area of a rectangle
The area of a rectangle $ A=l\times w $, where $ A $ is the area, $ l $ is the length, and $ w $ is the width. We know that $ A = 55.8 $ square inches and $ w = 4.5 $ inches. So our equation is $ 55.8=l\times4.5 $ or $ 4.5l=55.8 $
## Step2: Solve for $ l $ by dividing both sides by $ 4.5 $
$$
l=\frac{55.8}{4.5}
$$
## Step3: Simplify the division
$ \frac{55.8}{4.5}=12.4 $
## Check:
Substitute $ l = 12.4 $ and $ w = 4.5 $ into the area formula: $ A=12.4\times4.5 = 55.8 $ square inches, which matches the given area. So the solution is correct.
# Answer:
The length of the rectangle is $ 12.4 $ inches.

### 5. Solve $\boldsymbol{\frac{x}{-6}=-4}$
# Explanation:
## Step1: Isolate $ x $ by multiplying both sides by $ - 6 $
To solve for $ x $, we multiply both sides of the equation by $ -6 $.
$$
x=-4\times(-6)
$$
## Step2: Simplify the multiplication
$ -4\times(-6) = 24 $
## Check:
Substitute $ x = 24 $ back into the original equation:
Left - hand side: $ \frac{24}{-6}=-4 $
Since the left - hand side equals the right - hand side, the solution is correct.
# Answer:
$ x = 24 $

### 6. Solve $\boldsymbol{-1.4x = 7}$
# Explanation:
## Step1: Isolate $ x $ by dividing both sides by $ - 1.4 $
To solve for $ x $, we divide both sides of the equation by $ -1.4 $.
$$
x=\frac{7}{-1.4}
$$
## Step2: Simplify the division
$ \frac{7}{-1.4}=-5 $
## Check:
Substitute $ x=-5 $ back into the original equation:
Right - hand side: $ -1.4\times(-5)=7 $
Since the left - hand side ($ 7 $) equals the right - hand side, the solution is correct.
# Answer:
$ x=-5 $

### 7. Solve $\boldsymbol{\frac{8}{3}=\frac{2}{15}j}$
# Explanation:
## Step1: Isolate $ j $ by multiplying both sides by $ \frac{15}{2} $
To solve for $ j $, we multiply both sides of the equation by the reciprocal of $ \frac{2}{15} $, which is $ \frac{15}{2} $.
$$
\frac{8}{3}\times\frac{15}{2}=j
$$
## Step2: Simplify the left - hand side
$ \frac{8\times15}{3\times2}=\frac{120}{6}=20 $
## Check:
Substitute $ j = 20 $ back into the original equation:
Right - hand side: $ \frac{2}{15}\times20=\frac{40}{15}=\frac{8}{3} $
Since the left - hand side equals the right - hand side, the solution is correct.
# Answer:
$ j = 20 $

### 8. Solve $\boldsymbol{10=-2r}$
# Explanation:
## Step1: Isolate $ r $ by dividing both sides by $ - 2 $
To solve for $ r $, we divide both sides of the equation by $ -2 $.
$$
r=\frac{10}{-2}
$$
## Step2: Simplify the division
$ \frac{10}{-2}=-5 $
## Check:
Substitute $ r=-5 $ back into the original equation:
Right - hand side: $ -2\times(-5)=10 $
Since the left - hand side ($ 10 $) equals the right - hand side, the solution is correct.
# Answer:
$ r=-5 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. Solve $\boldsymbol{\frac{4}{3}=\frac{2}{15}j}$

Step1: Isolate \( j \) by multiplying both sides by \( \frac{15}{2} \)

Step2: Simplify the left - hand side

Check:

Step1: Isolate \( t \) by dividing both sides by \( 5.9 \)

Step2: Simplify the division

Check:

Step1: Isolate \( r \) by dividing both sides by \( - 2 \)

Step2: Simplify the division

Check:

Answer:

2. Solve $\boldsymbol{-23.6 = 5.9t}$