# Common Symbols in Algebra: Meanings & Applications

Instructor: Ellen Manchester
Mathematic symbols are key to unlocking the language of algebra and other branches of mathematics. In this lesson, we'll explore the meaning and applications behind algebraic symbols, after which your mathematical adventure will truly begin!

## Variables = Letters = Unknowns

In algebra, a variable is the use of a letter, usually x and y, to represent an unknown quantity. For instance, if you have 7 cookies, and you're left with 3 after your friends leave, algebra and the use of a variable can help you find out how many were eaten: 7 - x = 3, or x + 3 = 7.

Typically, the first symbol in an algebra problem is the letter, or variable. However, either form of the equation shown above can be used to translate a word problem into an algebraic equation.

## Symbols of Equality

Most of you are probably familiar with basic equals sign, which means 'the same as': =.

For instance, 3x - 2 = 4 means three times an unknown minus 2 is the same as 4.

The equal sign is important because it forms the balancing point or fulcrum of the equation. Whatever mathematical operation you perform on side of the equation, you must also perform on the other side.

In solving algebraic equations, you'll also come across an altered equal sign with three bars: In algebra, an altered equivalence symbol means: 'is identical to' or 'is equal by definition'. Another symbol that indicates a number or quantity is almost equal to another number or quantity is: As used here, the squiggly lines indicate that the numbers on either side of the equal sign are close to, but not exactly the same as, each other. So, if you wanted to find the value of the square root of 2 = 1.41421356…, you'd say the square root of 2 is about 1.4. When working with approximations, this equivalence symbol is the best one to use.

## Symbols of Inequality

We use inequality symbols when the solution has a range of answers. For instance, the difference between x = 4 and x > 4, is that x > 4 indicates all the numbers larger than 4 through infinity, while x = 4 only refers to the number 4.

Inequality symbols are read from left to right. When the smaller side appears first, it's the less than symbol. When the larger side appears first, it's the greater than symbol. For example, you'd use  Let's look at another example, if you owned a business and wanted to work no more than 50 hours per week, you'd use the 'less than or equal to' symbol and write it this way: ## Symbols of Organization

Parenthesis, brackets and braces help to keep algebraic equations organized and show which operation to perform first. Remember that, in algebra, we begin solving problems from the inside out, staring with the parentheses and then moving onto the brackets and braces. Let's use the order of operations to simplify this equation:

3{5(2-3) (4+1) - (6-7)} + 3: First, perform the calculations shown in parentheses.

3{5(-1) (5) - (-1)} + 3: Multiply the numbers inside the brackets or 5(-1).

3{5-5+1} + 3: Add the numbers inside the brackets or 5 + 1.

3{5[-4]} + 3: Multiply the numbers inside the braces or 5*(-4).

3{-20} + 3: Multiply 3 and -20.

-60+3: Add the remaining numbers.

-57: Solution

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