## Equations and Inequalities

In algebra, an**equation**is a mathematical expression that contains an equals sign. It tells us that two expressions represent the same number. For example, is an equation. An

**inequality**is a mathematical expression that contains inequality signs. For example, is an inequality. Inequalities are used to tell us that an expression is either larger or smaller than another expression. Equations and inequalities can contain both

**variables**and

**constants**.

Variables
are usually given a letter and they are used to represent unknown
values. These quantities can change because they depend on other numbers
in the problem.

Constants are quantities that remain unchanged. Ordinary numbers like and are constants.

Equations
and inequalities are used as a shorthand notation for situations that
involve numerical data. They are very useful because most problems
require several steps to arrive at a solution, and it becomes tedious to
repeatedly write out the situation in words.

### Write Equations and Inequalities

Here are some examples of equations:To write an inequality, we use the following symbols:

>

**greater than**

**greater than or equal to**

<

**less than**

**less than or equal to**

**not equal to**

Here are some examples of inequalities:

The
most important skill in algebra is the ability to translate a word
problem into the correct equation or inequality so you can find the
solution easily. The first two steps are

**defining the variables**and**translating**the word problem into a mathematical equation.**Defining the variables**means that we assign letters to any unknown quantities in the problem.

**Translating**means that we change the word expression into a mathematical expression containing variables and mathematical operations with an equal sign or an inequality sign.

**Example**

*Define the variables and translate the following expressions into equations.*

a) A number plus 12 is 20.

b) 9 less than twice a number is 33.

c) $20 was one quarter of the money spent on the pizza.

**Solution**

**Define**

Let the number we are seeking.

**Translate**

A number plus 12 is 20.

b)

**Define**

Let the number we are seeking.

**Translate**

9 less than twice a number is 33.

This means that twice the number, minus 9, is 33.

c)

**Define**

Let the money spent on the pizza.

**Translate**

$20 was one quarter of the money spent on the pizza.

Often word problems need to be reworded before you can write an equation.

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