**Unit 6.1: Solving Equations Using inverse operations**

**what we need to know**

**What is a numerical coefficient**

Variables

Equations

How to solve equations

Parts of a fraction: Numerator and Denominator

Variables

Equations

How to solve equations

Parts of a fraction: Numerator and Denominator

**more information**

**In this part of the unit, you will be learning and reviewing methods to solve linear equations. Throughout Junior high, you have done this in one way or another. So, do not worry... we got this!**

Before we dive into the different strategies to solve equations, let's review what IT IS to "solve" an equation:

Before we dive into the different strategies to solve equations, let's review what IT IS to "solve" an equation:

**Solving an equation means finding the value of the variable. To do this means that the variable MUST be isolated.***Isolating a variable*means doing all operations and manipulations possible as to end with the variable in one side of the equal sign, while all numbers end up on the other side of the equal sign.**You should always solve by using addition and subtraction BEFORE using multiplication and division.****Remeber: Whatever you do to one side, you do to the other side!****The variable must, when the equation is solved: Be by itself, have a numerical coefficient of 1, and be positive.****To check whether the solution you got is the correct one, substitute the value of the variable obtained into the original equation. If the solution is correct, an equality will be held. That is, both sides of the equal sign have the exact same numerical value.**

**Also important to remember (as this will become relevant very soon) that equations HAVE ONE SOLUTION ONLY.**

The new strategy presented in this sub-unit involves solving equations by using inverse operations. Take a look at the following set of notes for an explanation of inverse operations:

The new strategy presented in this sub-unit involves solving equations by using inverse operations. Take a look at the following set of notes for an explanation of inverse operations:

**solving equations using "the river" method**

**As I explained in class, this is the way I learned how to solve equztions way back then. Think about it as another tool, another way to solve equations.. Take a look at the explanation,, and if it works for you, USE IT! If not, move on the the other methods we will talk about and stick to the one you understand the most.**

9_6.1_-_solving_equations_-_the_river_method.pdf | |

File Size: | 4280 kb |

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**solving equations using inverse operations**

9_unit_6.1_-_solving_equations_using_inverse_operations.pdf | |

File Size: | 2344 kb |

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## solving equations with variables on both sides of the equal sign

**here is another example:**

**and another example:**

9_unit_6.1_-_solving_equations_-_variables_on_both_sides.pdf | |

File Size: | 1951 kb |

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**solving equations with fractional variables (the variable is in a fraction)**

**another example:**

**and another example:**

9_unit_6.1_-_solving_equations_-_variables_on_fractions.pdf | |

File Size: | 2175 kb |

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## solving equations involving the distributive property

9_unit_6.1_-_solving_equations_-_distributive_property.pdf | |

File Size: | 2067 kb |

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**videos that may help you**

**worksheets **

**Here are all the worksheets that were given to you in class, which you had to do before the quiz.:**

9_unit_6.1-6.2_worksheet.pdf | |

File Size: | 11682 kb |

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**And here the solutions to each of the worksheets for each specific topic:**

**Solutions to solving equations using inverse operations:**

9_unit_6.1_-_worksheet_solutions__-_inverse_operations.pdf | |

File Size: | 3666 kb |

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Solutions to equations with

**variables on both sides of the equal sign:** 9_unit_6.1_-_worksheet_solutions__-_variables_on_both_sides.pdf | |

File Size: | 7653 kb |

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Solutions to

**equations with the variable in a fraction:** 9_unit_6.1_-_worksheet_solutions__-_variables_in_fractions.compressed.pdf | |

File Size: | 1060 kb |

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Solutions to

**equations with the distributive property:** 9_unit_6.1_-_worksheet_solutions__-_distributive_property.pdf | |

File Size: | 7680 kb |

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Solutions to

**last page of worksheet - Methods of choice:** 9_unit_6.1_-_worksheet_solutions__-_method_of_choice.pdf | |

File Size: | 5459 kb |

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**review - workbook**

workbook_-_unit_6.1.pdf | |

File Size: | 4225 kb |

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