I need a definition of all of these terms in math

Question

addition property of equality
division property of equality
equation
equivalent equations
formula
identity
inductive reasoning
inverse operations
isolate
literal equation
multiplication property of equality
open sentence
solution to an equation
subtraction property of equality

Answer 1

1. Addition Property of Equality: This property states that if you add the same number to both sides of an equation, then the statement remains true. For example, if a = b, then a + c = b + c.

2. Division Property of Equality: This property states that if you divide both sides of an equation by the same non-zero number, then the statement remains true. For example, if a = b, then a/c = b/c (c ≠ 0).

3. Equation: An equation is a mathematical statement that shows that two expressions are equal. It consists of an equality sign (=) in between two expressions. For example, 2x + 3 = 7 is an equation.

4. Equivalent Equations: Equivalent equations are different equations that have the same solution. They are obtained by performing the same operation on both sides of the equation. For example, 2x + 3 = 7 and 2x = 7 - 3 are equivalent equations.

5. Formula: A formula is a mathematical relationship or rule expressed using symbols and variables. It is used to solve specific problems and is often represented by an equation. For example, the formula for the area of a rectangle is A = length × width.

6. Identity: An identity is an equation that is true for all values of its variables. It does not require any specific condition to be satisfied. For example, x + 0 = x is an identity.

7. Inductive Reasoning: Inductive reasoning is a method of reasoning that involves making general conclusions based on observed patterns or examples. It is used to form conjectures or hypotheses about mathematical relationships.

8. Inverse Operations: Inverse operations are operations that "undo" each other. For example, addition and subtraction are inverse operations, as are multiplication and division. Using inverse operations allows you to isolate a variable in an equation.

9. Isolate: To isolate a variable in an equation means to rearrange the equation so that the variable is on one side and all other terms are on the other side. This allows you to easily solve for the variable.

10. Literal Equation: A literal equation is an equation that contains multiple variables or symbols. It is used to represent a relationship between different quantities. For example, the formula for the Pythagorean theorem (a² + b² = c²) is a literal equation.

11. Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, then the statement remains true. For example, if a = b, then ac = bc (c ≠ 0).

12. Open Sentence: An open sentence is a statement that contains one or more variables and does not become a true or false statement until specific values are assigned to the variables. It is an equation or inequality with variables.

13. Solution to an Equation: A solution to an equation is a value or values that make the equation true. When you substitute a solution into an equation, both sides of the equation should be equal.

14. Subtraction Property of Equality: This property states that if you subtract the same number from both sides of an equation, then the statement remains true. For example, if a = b, then a - c = b - c.