Day 9

ZAP TOMORROW AT LUNCH!

Algebra: Chapter 1-7

Solving Equations, An Introduction

An EQUATION is a mathematical sentence that uses the equal sign to state that 2 expressions represent the same number or are equivalent. An equation that contains at least 1 variable is called an OPEN SENTENCE.

The set of numbers from which you can select replacements for the variable is called the REPLACEMENT SET, usually noted with squiggly brackets {2, 5, 12}. A replacement for a variable that makes an equation true is called the SOLUTION. To SOLVE and equation means to find all of its solutions. The collection of all the solutions is called the SOLUTION SET, usually contained in the { brackets}.

2 equations are EQUIVALENT if one can be obtained from the others by a sequence of adding, subtracting, multiplying or dividing from both sides of an equation.

Intro to Algebra: Chapter 1-5

The Distributive Property of Multiplication over Addition

The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac

${\displaystyle }$For example: `3(x+2)=3x+6`

${\displaystyle \mathrm{}}$The opposite of distribution is factoring where we go backward. For example: `3x+3y=3(x+y)`

${\displaystyle \mathrm{}\mathrm{}\mathrm{}}$In an expression like

${\displaystyle 6s+6t+6\mathrm{w,}}$the 6s, 6t and 6w are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!

You can collect like terms, for example: `6y+2y` is the same as `8y`

${\displaystyle \mathrm{}}$ ${\displaystyle }$ ${\displaystyle \mathrm{}}$Try these 2 links from purplemath.com, this one for distribution and this one for factoring.