Equations vs Inequalities
Have you ever wondered how a sentence can be a statement or a question? Could you write a sentence that would work with both a period and a question mark?
What are equations and inequalities?
Math is a language that uses symbols to represent the world around us. In math our sentences are constructed by two expressions and a symbol, to compare the two expressions. The two types of sentences that can be written in math are an EQUATION or an INEQUALITY.
Math Equations
An equation is anytime there are two things that are equivalent to each other. Equivalent is another way to say equal or the same. In math we create expressions to represent situations or things in our everyday life. So, a more formal math definition of an equation would be an equation is two equivalent or equal expressions.
Math Equation.pdfSo, what about when two expressions are not equal to each other?
Math Inequalities
An inequality is anytime two expressions are being compared to each other.
Math Inequality.pdfIf you forgot what an expression is, check out the fundamental Parts of an Expression and Simplifying Expressions!
How do you identify an equation vs an inequality?
When comparing expressions there are 6 ways to compare any two expressions. The equal sign is used for equations only and the other 5 symbols are used for inequalities.
How do you identify an equation vs an inequality.pdfIdentifying an equation or inequality from a graph
Identifying an equation or inequality from a graph.pdfWhy do we learn about equations and inequalities?
In life, some situations have an exact value for its solution, while other situations don’t have an exact value but instead a range of accepted values for its solution. In math the equal sign is used in the cases where there is an exact value for the solution and inequality signs are used for when there are a range of accepted values for the solution. Some examples to highlight where an exact value is desired vs a range of values is desired includes:
1) You want to run a mile faster than 8 minutes: any time less than 8 minutes meets this goal
vs.
You want to run a mile in exactly 8 minutes: only one time meets this goal, 8 minutes
2) You are shopping and a sales rack has a sign that reads ‘all items are $9.99 and up!’: only one item on the rack must be $9.99 to make this a true statement, all other items can cost more than $9.99
vs.
You are shopping and a sales rack has a sign that reads ‘all items are $9.99!’: the only option for the price of an item on this rack is $9.99
3) What about the situation of an airline ticket sale that states all flights from your city are only $49 and up! How many tickets must cost $49 for this statement to be true? Sadly, just one.
Mathematics is the language used to explain the world in which we live. The equal sign was developed to represent when a situation has only one exact outcome vs. inequality signs were developed to represent when a situation has a range of accepted outcomes. All mathematics was developed at some time in our past to model a situation and from these models we can now explain new and different situations.
What’s next? To see equations and inequalities in action check out the fundamentals Solving 1-Variable Equations: variable on one side of the equation; Solving 1-Variable Equations: variable on both sides of the equation; and Solving 1-Variable Inequalities!
