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# Kiosk

The order and connection
of ideas
is the same as the order and connection of things. Baruch (Benedict) Spinoza
1623 - 1677 Dutch philospher |

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) |

**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 |

Evaluating algebraic expressions (PEMDAS) | Creating and developing spreadsheets |

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