What is an equation that contains one or more variables and may be true or false depending on the value of its variable?

An open sentence is defined as an equation that contains one or more variables and its truth value can change based on the values assigned to those variables. For example, in the equation ( x + 3 = 10 ), the truth of this statement depends on the value of ( x ). If ( x ) is 7, the equation is true; if ( x ) is 5, the equation is false. This characteristic of having variables that can take on different values makes an open sentence distinct from other terms.

In comparison, a constant refers to a fixed value that does not change, which lacks any variables. An expression consists of numbers and operations but does not include an equals sign and therefore does not convey a relationship like an equation does. An equation is a broader term that simply states that two expressions are equal, but without the variable component affecting the truth value, it does not capture the essence of an open sentence. Thus, the correct identification of an equation that can be true or false depending on variable values is specifically characterized as an open sentence.