Your Study Guides and Strategies starts here!

The order and connection

of ideas

is the same as the order

and connection of things.

of ideas

is the same as the order

and connection of things.

Baruch (Benedict) Spinoza

1623 - 1677 Dutch philospher

1623 - 1677 Dutch philospher

folder menus

but any letter will do!

Variable(s) in linear expressions

- Cannot have exponents (or powers)

For example,squared or**x**2**x** - Cannot multiply or divide each other

For example: "x" times "y" or xy; "x" divided by "y" or x/y - Cannot be found under a root sign or square root sign (sqrt)

For example: √x or the "square root x"; sqrt (x)

functions of addition, subtraction, multiplication, and division

**These are examples of linear expressions:**

x + 4 | 2x + 4 | 2x + 4y |

**These are not linear expressions:**

x2 | (no exponents on variables) | |

2xy + 4 | (can't multiply two variables) | |

2x / 4y | (can't divide two variables) | |

√x | (no square root sign on variables) |

Solve these linear equations by clicking and dragging

a number to the "other" side of the equal sign.

Remember that you are "isolating" the unknown "X" to solve the problem.

(More examples are provided below.)

**Find x if: 2x + 4 =
10**

1. |
Isolate "x" to one side of the equation
by subtracting 4 from both sides: |
2x + 4 - 4 = 10 - 4 2x = 6 |

2. |
Divide both sides by 2: |
2x / 2 = 6 / 2 x = 3 |

3. |
Check your work with the original equation: |
2x + 4 = 10 (2 * 3) + 4 = 10 6 + 4 = 10 |

**
Find x if:
** **3x - 4 =
-10**

(using negatives)

1. |
Isolate "x" to
one side of the equation
by adding 4 to both sides: |
3x
- 4 + 4 = -10 + 4 3x = -6 |

2. | Divide both sides by 3: | 3x
/ 3 = -6 / 3 x = -2 |

3. |
Check your work with the original equation: | (3
* -2) - 4 = -10 -6 - 4 = -10 |

**Find x if: 4x - 4y = 8**

(using more than one variable)

1. |
First step is to isolate "x"
to one side of the equation by adding 4y to both sides: |
4x - 4y + 4y = 8 + 4y 4x = 8 + 4y |

2. | Second step is to divide both sides by 4: |
4x / 4 = (8 + 4y) / 4 x = 2 + y |

3. |
Check your work with the original equation: |
4 * (2 + y) - 4y = 8 8 + 4y - 4y = 8 8 = 8 |

Find x if:
*x + 32 = 12*

Note: since the square is on the*number *and not on the variable,

the expression qualifies as a linear expression

Note: since the square is on the

the expression qualifies as a linear expression

1. | First step is to square the number: |
x + 32 = 12 x + 9 = 12 |

2. |
Second step is to subtract both sides by 9: |
x + 9 - 9 = 12 - 9 x = 3 |

3. |
Check your work with the original equation: |
3 + 32 = 12 3 + 9 = 12 12 = 12 |

Word problems, exercise I | Word problems, II | Word problems, III |

Evaluating algebraic expressions | Creating and developing spreadsheets |

P.E.M.D.A.S.: 2nd exercise | P.E.M.D.A.S.: 3rd exercise | Sudoku 数独