I need a definition of all of these terms

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

Addition Property of Equality: This property states that when the same value is added to both sides of an equation, the two sides remain equal. For example, if 3 + x = 7, the addition property of equality allows us to add -3 to both sides to get x = 4.

Division Property of Equality: This property states that when the same non-zero value is divided from both sides of an equation, the two sides remain equal. For example, if x/5 = 6, the division property of equality allows us to multiply both sides by 5 to get x = 30.

Equation: An equation is a mathematical statement that contains an equals sign (=) and shows that two expressions are equal. For example, 2x + 3 = 9 is an equation.

Equivalent Equations: Equivalent equations are two or more equations that have the same solution. They may look different, but they represent the same mathematical relationship. For example, x = 5 and 2x = 10 are equivalent equations.

Formula: A formula is a mathematical relationship or equation that expresses a rule or principle. Formulas are commonly used to calculate specific values or solve problems in different areas of mathematics and science. Examples include the formula for the area of a circle (A = πr²) or the formula for the quadratic equation.

Identity: In mathematics, an identity is an equation that is true for all values of the variable. For example, 2x + 3x = 5x is an identity because it holds true regardless of the value of x.

Inductive Reasoning: Inductive reasoning is a logical process of making generalized conclusions based on specific observations or examples. It involves using patterns and evidence to form a hypothesis or general rule, although the conclusion may not be guaranteed to be true. For example, after observing that the first five numbers in a sequence are 1, 4, 9, 16, 25, one may use inductive reasoning to hypothesize that the next number is 36.

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 is a common strategy to solve equations by isolating the variable.

Isolate: In the context of solving equations, isolating a variable means to get it alone on one side of the equation. The goal is to rearrange the equation using various operations so that the variable is separated from the other terms or numbers.

Literal Equation: A literal equation is an equation that contains two or more variables. Literal equations are commonly used in mathematics and science to represent relationships between different quantities. For example, the equation V = lwh represents the volume (V) of a rectangular prism in terms of its length (l), width (w), and height (h).

Multiplication Property of Equality: This property states that when both sides of an equation are multiplied by the same non-zero value, the two sides remain equal. For example, if 4x = 12, the multiplication property of equality allows us to divide both sides by 4 to get x = 3.

Open Sentence: An open sentence is a statement that contains one or more variables and becomes a true or false statement when specific values are substituted for the variables. For example, x + 3 = 7 is an open sentence because it becomes true when x is replaced by 4.

Solution to an Equation: A solution to an equation is a value or set of values that make the equation true. For example, in the equation 2x + 5 = 11, the value x = 3 is a solution because when we substitute 3 for x, the equation holds true.

Subtraction Property of Equality: This property states that when the same value is subtracted from both sides of an equation, the two sides remain equal. For example, if x + 2 = 8, the subtraction property of equality allows us to subtract 2 from both sides to get x = 6.