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In an equation with one variable, the variable has a solution, or value, that makes the equation true.
Explain what an equation in one variable represents and the reasons for using one
A value that can be substituted for a variable to make an equation true.
A variable in an equation that needs to be solved for.
A mathematical statement that asserts the equivalence of two expressions.
An
equation is a mathematical statement that asserts the equivalence of two
expressions. For example, the assertion that "two plus five equals seven" is represented by the equation
In many cases, an equation contains one or more variables. These are still written by placing each expression on either side
of an equals sign (
It is possible for equations to have more than one variable. For example,
When an equation contains a variable such as
For example, consider the equation we were talking about above:
The values of the variables that make an equation true are called the solutions of the equation. In turn, solving an equation means determining what values for the variables make the equation a true statement.
The equation above was fairly straightforward; it was easy for us to identify the solution as
If a number is found as a solution to an equation, then substituting that number back into the place of the variable should make the equation true. Thus, we can easily check whether a number is a genuine solution to a given equation.
For example, let's examine whether
Substituting 3 for
This equality is a true statement. Therefore, we can conclude that
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Source: Boundless. “What is an Equation?.” Boundless Algebra Boundless, 01 Nov. 2016. Retrieved 23 Mar. 2017 from https://www.boundless.com/algebra/textbooks/boundless-algebra-textbook/introduction-to-equations-inequalities-and-graphing-2/introduction-to-equations-17/what-is-an-equation-372-17416/