What is an open sentence in math?

Answer 1

Every sentence to which standard logic applies has exactly one of the truth values (that is, either true or false, but not both). No sentence can be both true and false.
An equation is a statement that sets two mathematical expressions equal.
When both sides of an equation are numerical expressions (contain no variables), the equation is a closed statement. This means the equation can be assigned a truth value.
Example:
2 + 5 = 7 true 2(3) - 2 = 6 false
If an equation is neither true nor false, the equation is an open sentence.
An open sentence is a mathematical statement with one or more variables. When variables are present in an equation, the solution is unknown. The set of numbers that you use to represent the variable(s) is called the replacement set. The solution set is found when any value(s) for the variable from the replacement set makes the equation a true statement.

Examples: 3x+6=20; 12n-5=45; 6a+2b+7c=84; 4p>25; 9s+24<65+2s.

To solve one you have to find the value of the variable.
If an equation is true for all values of the variables involved, then it is called an identity. For example 4(x -3) = 4x - 12.
If an equation is true only for some values, then it is called a conditional equation. For example, x^2 - 3x - 4 = 0 is only true when x = -1 or x = 4, which are called the roots of there

by emile lefer a 10 year old