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2001-C: Symbolic Algebra 1

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2001-C: Symbolic Algebra 1

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Symbols like \( x \), \( y \), and \( z \) can be manipulated just like numbers can. You can add, subtract, multiply, or divide both sides of an equation by a symbol. To Solve for a variable means that you have only that variable on one side of the equation.

For example, let's say that I have an equation like this: $$ Z = X Y^2 + Y^3 X + (Y - X) XY $$ This equation would be referred to as "\( Z \) in terms of \( X \) and \( Y \)".

Imagine you have \( Z = \text{some long function that includes } X \text{ and } Y. \) Imagine that you are able to manipulate the equation so that instead, it looks like this: \( Y = \text{some long function that includes } Z \text{ and } X. \) This is called "Solving for \( Y \) in terms of \( X \) and \( Z \)."

  1. Solve for \( B \):
    \( A = B C \)
  2. Solve for \( E \):
    \( D = E + F \)
  3. Solve for \( G \):
    \( H = G - I \)
  4. Solve for \( N \):
    \( M = \frac{N}{O} \)
  5. Solve for \( Q \):
    \( P = 5 Q \)
  6. Solve for \( L \):
    \( J = K - L \)
  7. Solve for \( R \):
    \( \frac{S}{R} = T \)
  8. Solve for \( m \):
    \( E = mgh \)
  9. Solve for \( h \):
    \( E = mgh \)
  10. Solve for \( m \):
    \( E = \frac{1}{2} m v^2 \)
  11. Solve for \( v \). Note that there are two solutions.
    \( E = \frac{1}{2} m v^2 \)
  12. Solve for \( F_1 \):
    \( F_1 - F_2 = m a \)
  13. Solve for \( a \):
    \( F_1 - F_2 = ma \)
  14. Solve for \( v_i \):
    \( v_f = v_i + at \)
  15. Solve for \( a \):
    \( v_f = v_i + at \)
  16. Solve for \( t \):
    \( v_f = v_i + at \)
  17. Solve for \( v \). Note that there are two solutions.
    \( a = \pm \frac{v^2}{r} \)
  18. Solve for \( r \):
    \( a = \frac{v^2}{r} \)
  19. Solve for \( m_1 \):
    \( F = \frac{G m_1 m_2}{r^2} \)
  20. Solve for \( m_2 \):
    \( F = \frac{G m_1 m_2}{r^2} \)
  21. Solve for \( r \). Note that there are two solutions :
    \( F = \frac{G m_1 m_2}{r^2} \)

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