Question

1. ( b = k - tn ); for ( n ) 18) ( 3x + 4 = 16 ); for ( x ) 19) ( b = e + \frac{3d}{n} ); for ( n ) 20) ( b = tn - b ); for ( n ) 21) ( w = \frac{a + e}{x} ); for ( x ) 22) ( zm = x + y ); for ( x ) 23) ( n + ka = ha ); for ( a ) 24) ( u = kx + px ); for ( x ) 25) ( u = 3b - 2a + 3 ); for ( a ) 26) ( s = 9a - 9 - 3b ); for ( a ) 27) ( y = 4ea - 3ba ); for ( a ) 28) ( -3a - 3 = -2n + 3p ); for ( a ) 29) ( 4x = -4r + 2d ); for ( x ) 30) ( n = \frac{-3a - 3}{ka} ); for ( a )

Explanation:

Let's solve problem 29: \( 4x = -4p + 2d \), for \( x \).

Step 1: Isolate \( x \)

To solve for \( x \), we need to divide both sides of the equation by 4.
\[
\frac{4x}{4} = \frac{-4p + 2d}{4}
\]

Step 2: Simplify both sides

Simplify the left side: \( \frac{4x}{4} = x \).
Simplify the right side: We can factor out a 2 from the numerator: \( \frac{2(-2p + d)}{4} \), then simplify the fraction by dividing numerator and denominator by 2: \( \frac{-2p + d}{2} \), or we can split the fraction: \( \frac{-4p}{4} + \frac{2d}{4} = -p + \frac{d}{2} \). Both forms are correct, but let's use the first simplification.
\[
x = \frac{-4p + 2d}{4} = \frac{-2p + d}{2} \quad \text{(or)} \quad x = -p + \frac{d}{2}
\]

Answer:

\( x = \frac{-2p + d}{2} \) (or \( x = -p + \frac{d}{2} \))