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Patterns: Variables, Expressions, & Equations

Solving for "x"

Sometimes you will have to find out what x is, In order to do that you have to do the opposite operation on the other side of the equal sign. For instance:

x - 2 = 6

x = 6 + 2

x + 5 = 10

x = 10 - 5

3x = 30

x = 30/3

Algebra

Variable

Word Problems

Algebra is the language through which we describe patterns. It is almost like a shortcut! As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. Algebra typically deals with expressions and equations.

An equation is a set of numbers which equal the exact amount. ei. 2 + 2 =4 or 2 x 3 = 6

An expression (algebraic expression) is a combination of numbers and variables (letters) which represent a a pattern. expression do not have an equal sign.

A variable is a symbol for a number we don't know yet. It is usually a letter like x or y. Expressions can incorporate any operation (plus, minus, times, divide)

Example: x + 2 = 6, x is the variable.

x - 2 = 6

3x = 6

x/2 = 6

Addition Words - Add, Altogether, Both, In all, Sum, Total

Subtraction Words - Difference, Fewer, How many more, How much more, Left, Less, Minus, Need to, Remains, Words ending with "er"; higher, longer, faster, heavier, larger, shorter, slower, farther, etc.

Multiplication Words - Times, , At this rate, each

Division Words - Each

Example

For instance: 7, 8, 9, 10, 11 Can translate into the pattern rule - start at 7 and add 1 each time. Putting this pattern into a chart will help us understand it more. When you put this pattern into a chart you can start to see a clear pattern. Now we have to choose one of the columns as a variable. the other column will represent the algebraic expression. Can you think of an expression for the following pattern?

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