Which x satisfies an equation

Learning Objectives Define what it means for a value to 'satisfy' an equation. Substitute a given numerical value for a variable into an algebraic equation. Evaluate both sides of an equation after substituting a value for the variable. Determine if a given value is a solution to a linear equation by checking if it makes the equation true. Explain why a specific value does or does not satisfy a given equation. Distinguish between an algebraic expression and an algebraic equation. Ever wonder if a secret code can unlock a treasure chest? 🗝️ In math, we'll learn how to check if a specific number is the 'key' that makes an equation true! In this lesson, you'll discover what it means for a number to 'satisfy' an equation. This fundamental...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, typically separated by an equals sign (=).$$2x + 3 = 7$$ VariableA symbol, usually a letter, that represents an unknown numerical value in an expression or equation.In $2x + 3 = 7$, 'x' is the variable. ExpressionA combination of numbers, variables, and operation symbols, but without an equals sign.$$2x + 3$$ is an expression. Satisfy an EquationA value for a variable 'satisfies' an equation if, when substituted into the equation, it makes the equation a true statement (both sides are equal).If $x=2$ satisfies $2x=4$, because $2(2)=4$ is true. SolutionA specific value for the variable that makes an equation true; it is the value that satisfies the equation.For $2x + 3 = 7$, the...

The Definition of Satisfying an Equation A value $v$ satisfies an equation if, when $v$ is substituted for the variable in the equation, the left side of the equation equals the right side of the equation. This rule defines what it means for a number to be a 'solution' or to 'satisfy' an equation. It's the fundamental test you perform. The Substitution Principle for Equations To check if a value $v$ satisfies an equation, replace every instance of the variable (e.g., $x$) with $v$ and then evaluate both sides of the equation independently. This principle guides the process of checking. Always substitute the value for ALL occurrences of the variable and then simplify each side separately before comparing.