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15) $g = b + \\frac{m}{a}$, for $a$ 16) $g = x - c + y$, for $x$ 17) $g…

Question

  1. $g = b + \frac{m}{a}$, for $a$
  2. $g = x - c + y$, for $x$
  3. $g = b - ca$, for $a$
  4. $g = ca - b$, for $a$
  5. $2x + 4 = xg$, for $x$
  6. $g = \frac{1 + 2a}{a}$, for $a$
  7. $g = \frac{x - c}{x}$, for $x$
  8. $xm = x + z$, for $x$
  9. $u + ka = ba$, for $a$
  10. $u = kx + yx$, for $x$
  11. $u = 3b - 2a + 2$, for $a$
  12. $z = 9a - 9 - 3b$, for $a$
  13. $g = 4ca - 3ba$, for $a$
  14. $-3a - 3 = -2n + 3p$, for $a$
  15. $4x = -4r + 2d$, for $x$
  16. $u = \frac{-2a - 3}{ka}$, for $a$

Explanation:

Response

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

Step 1: Isolate \( x \)

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

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: \( \frac{2(-2r + d)}{4} \), then simplify the fraction by dividing numerator and denominator by 2: \( \frac{-2r + d}{2} \) or we can split the fraction: \( \frac{-4r}{4} + \frac{2d}{4} = -r + \frac{d}{2} \)

Answer:

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