# Rearranging Algebra Expressions

rename
Updated
2009-06-05 19:51

## Rearranging Algebra Expressions

In each of the following, rearrange the equation listed on the left to isolate z.

Original Equation | Equation for z |
---|---|

3 - 5 + 2 = 4 z | z = 0 |

5 - 3 + 2 z = 4 | z = 1 |

7 z - 3 z + 4 = 0 | z = -1 |

8 z - 3 = 4 z + 3 | z = 3/2 |

z^{2} + 4 z + 4 = 0 | z = -2 |

z^{2} - 6 z+ 9 = 0 | z = 3 |

In each of the following, rearrange the equation listed on the left to isolate Z.

Original Equation | Equation for Z |
---|---|

A - B = Y × Z | Z = (A - B) / Y |

A + B = Y + Z | Z = A + B - Y |

A + B + Y + Z = 0 | Z = -A - B - Y |

(A × Z) + (B × Y) = 0 | Z = -B × Y / A |

A = Z × Y / B | Z = B × A / Y |

A + (Z/Y) = B | Z = (B - A) × Y |

A + B = sin(Z/Y) | Z = Y × sin^{-1}(A + B) |

Y = A × cos(Z + B) | Z = -B + cos^{-1}(Y/A) |

A = B × Z^{Y} | Z = (A/B)^{(1/Y)} |

A = B × exp(Z - Y) | Z = Y + ln(A/B) |

Y = A / (Z-B)^{2} | Z = B ± sqrt(A/Y) |

(Y/A)^{2} + (Z/B)^{2} = 1 | Z = ±B × sqrt(1 - (Y/A)^{2}) |

Question | Answer |
---|---|

A-B=Y×Z | Z=(A-B)/Y |

A+B=Y+Z | Z=A+B-Y |

A+B+Y+Z=0 | Z=-A-B-Y |

(A×Z)+(B×Y)=0 | Z=-B×Y/A |

A=Z×Y/B | Z=B×A/Y |

A+(Z/Y)=B | Z=(B-A)×Y |

A+B=sin(Z/Y) | Z=Y×sin^{-1}(A+B) |

Y=A×cos(Z+B) | Z=-B+cos^{-1}(Y/A) |

A=B×Z^{Y} | Z=(A/B)^{(1/Y)} |

A=B×exp(Z-Y) | Z=Y+ln(A/B) |

Y=A/(Z-B)^{2} | Z=B±sqrt(A/Y) |

(Y/A)^{2}+(Z/B)^{2}=1 | Z=±B×sqrt(1-(Y/A)^{2}) |