Question

1. solve for the indicated variable. show all work.

a) ( v = lwh ) solve for ( w ).
b) ( y = mx + b ) solve for ( x ).

1. 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 )

Explanation:

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

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:

$$ w=\frac{V}{lh} $$

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:

$$ x=\frac{y - b}{m} $$

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:

\( w = \frac{V}{lh} \)

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