How the equation becomes true is given below.
Step-by-step explanation:
In an equation with one variable, the variable has a solution, or value, that makes the equation true.
- An equation is a mathematical statement that asserts the equivalence of two expressions.
- When an equation contains a variable, such as x
, the variable is considered an unknown value.
- The values of the variables that make the equation true are the solutions of the equation and can be found by solving the equation.
- A solution of an equation can be verified, or checked, by substituting in its value for the variable in the equation.
For example, the assertion that “two plus five equals seven” is represented by the equation 2
+
5
=7
.
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 (
=
). For example, the equation x
+
3
=
5
, read “
x plus three equals five”, asserts that the expression x
+
3 is equal to the value 5.
When an equation contains a variable such as x
, this variable is considered an unknown value. In many cases, we can find the possible values for x that would make the equation true. For example, consider the equation we were talking about above: x
+
3
=
5
. You have probably already guessed that the only possible value of x is 2, because you know that 2
+
3
=
5 is a true equation. We use an equals sign to show that we know the value of a given variable. In this case, we write x
=
2 (read as “
x equals two”).
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 x
=
2
.
