20. solve for the indicated variable. show all work.
a) ( v = lwh ) solve for ( w ).
b) ( y = mx + b ) solve for ( x ).
21. a - h) solve each equation. if there is no solution, write no solution. if there are infinite solutions, write identity. show all work.
a) ( 6v - 4 = -3v + 59 )
b) ( -t + 7 = 3t + 15 )
c) ( \frac{2n + 2}{8} = \frac{n}{3} )
d) ( 9(g - 4) = 2g - 1 )

Question

Accepted Answer

### Problem 20a: Solve $ V = lwh $ for $ w $
# Explanation:
## Step 1: Isolate $ w $
To solve for $ w $, we divide both sides of the equation by $ lh $ (assuming $ l
eq 0 $ and $ h
eq 0 $) to isolate $ w $.
$$
\frac{V}{lh} = \frac{lwh}{lh}
$$
## Step 2: Simplify
Simplifying the right - hand side, the $ l $ and $ h $ in the numerator and denominator cancel out, leaving us with:
$$
w=\frac{V}{lh}
$$
# Answer:
$ w = \frac{V}{lh} $

### Problem 20b: Solve $ y=mx + b $ for $ x $
# Explanation:
## Step 1: Subtract $ b $ from both sides
We want to get the term with $ x $ alone on one side. So we subtract $ b $ from both sides of the equation:
$$
y - b=mx + b - b
$$
Simplifying the right - hand side, $ b - b = 0 $, so we have:
$$
y - b=mx
$$
## Step 2: Divide by $ m $ (assuming $ m
eq0 $)
To solve for $ x $, we divide both sides of the equation by $ m $:
$$
\frac{y - b}{m}=\frac{mx}{m}
$$
Simplifying the right - hand side, the $ m $ in the numerator and denominator cancels out, giving:
$$
x=\frac{y - b}{m}
$$
# Answer:
$ x=\frac{y - b}{m} $

### Problem 21a: Solve $ 6v-4=-3v + 59 $
# Explanation:
## Step 1: Add $ 3v $ to both sides
We want to get all the $ v $ terms on one side. Adding $ 3v $ to both sides:
$$
6v+3v-4=-3v + 3v+59
$$
Simplifying both sides, $ 6v + 3v=9v $ and $ - 3v+3v = 0 $, so we have:
$$
9v-4 = 59
$$
## Step 2: Add 4 to both sides
To isolate the term with $ v $, we add 4 to both sides:
$$
9v-4 + 4=59 + 4
$$
Simplifying, $ - 4+4 = 0 $ and $ 59 + 4=63 $, so:
$$
9v=63
$$
## Step 3: Divide by 9
Divide both sides by 9 to solve for $ v $:
$$
v=\frac{63}{9}=7
$$
# Answer:
$ v = 7 $

### Problem 21b: Solve $ -t + 7=3t+15 $
# Explanation:
## Step 1: Add $ t $ to both sides
We want to get all the $ t $ terms on one side. Adding $ t $ to both sides:
$$
-t+t + 7=3t+t+15
$$
Simplifying, $ -t + t=0 $ and $ 3t + t = 4t $, so:
$$
7=4t + 15
$$
## Step 2: Subtract 15 from both sides
To isolate the term with $ t $, we subtract 15 from both sides:
$$
7-15=4t+15 - 15
$$
Simplifying, $ 7-15=-8 $ and $ 15 - 15 = 0 $, so:
$$
-8 = 4t
$$
## Step 3: Divide by 4
Divide both sides by 4 to solve for $ t $:
$$
t=\frac{-8}{4}=-2
$$
# Answer:
$ t=-2 $

### Problem 21c: Solve $ \frac{2n + 2}{8}=\frac{n}{3} $
# Explanation:
## Step 1: Cross - multiply
To eliminate the fractions, we cross - multiply. That is, we multiply the numerator of the left - hand side by the denominator of the right - hand side and set it equal to the numerator of the right - hand side multiplied by the denominator of the left - hand side:
$$
3(2n + 2)=8n
$$
## Step 2: Distribute the 3
Using the distributive property $ a(b + c)=ab+ac $ on the left - hand side:
$$
6n+6 = 8n
$$
## Step 3: Subtract $ 6n $ from both sides
To get all the $ n $ terms on one side:
$$
6n-6n + 6=8n-6n
$$
Simplifying, $ 6n-6n = 0 $ and $ 8n-6n = 2n $, so:
$$
6 = 2n
$$
## Step 4: Divide by 2
Divide both sides by 2 to solve for $ n $:
$$
n=\frac{6}{2}=3
$$
# Answer:
$ n = 3 $

### Problem 21d: Solve $ 9(g - 4)=2g-1 $
# Explanation:
## Step 1: Distribute the 9
Using the distributive property $ a(b - c)=ab - ac $ on the left - hand side:
$$
9g-36=2g-1
$$
## Step 2: Subtract $ 2g $ from both sides
To get all the $ g $ terms on one side:
$$
9g-2g-36=2g-2g-1
$$
Simplifying, $ 9g - 2g=7g $ and $ 2g-2g = 0 $, so:
$$
7g-36=-1
$$
## Step 3: Add 36 to both sides
To isolate the term with $ g $:
$$
7g-36 + 36=-1 + 36
$$
Simplifying, $ -36 + 36 = 0 $ and $ -1+36 = 35 $, so:
$$
7g=35
$$
## Step 4: Divide by 7
Divide both sides by 7 to solve for $ g $:
$$
g=\frac{35}{7}=5
$$
# Answer:
$ g = 5 $

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QUESTION IMAGE

Question

Explanation:

Problem 20a: Solve \( V = lwh \) for \( w \)

Step 1: Isolate \( w \)

Step 2: Simplify

Step 1: Subtract \( b \) from both sides

Step 2: Divide by \( m \) (assuming \( m

Step 1: Add \( 3v \) to both sides

Step 2: Add 4 to both sides

Step 3: Divide by 9

Answer:

Problem 20b: Solve \( y=mx + b \) for \( x \)