Does x satisfy an equation?

Learning Objectives Define what it means for a value to 'satisfy' an equation. Substitute a given numerical value for a variable in an equation. Evaluate both sides of an equation after substitution using the correct order of operations. Determine if the numerical value makes the equation true or false. Identify whether a given value is a solution to a simple linear equation. Explain the process of checking a solution to a peer. Ever wonder if a secret code works? 🕵️‍♀️ In math, we'll learn how to check if a number is the 'secret key' that makes an equation true! In this lesson, you'll discover how to test if a specific number fits perfectly into an equation, making both sides equal. This skill is crucial for understanding how equations work an...

TermDefinitionExample EquationA mathematical statement that shows two expressions are equal, separated by an equals sign (=).$3x + 5 = 11$ VariableA symbol, usually a letter (like x, y, or a), that represents an unknown numerical value.In $2y - 4 = 6$, 'y' is the variable. ExpressionA combination of numbers, variables, and operation symbols (like +, -, ×, ÷) that does not contain an equals sign.$5x + 2$ or $7 - y$ SubstituteTo replace a variable in an expression or equation with a specific numerical value.If $x=4$, substitute 4 for x in $2x+1$ to get $2(4)+1$. Satisfy an EquationWhen a numerical value, substituted for the variable, makes both sides of the equation equal, resulting in a true statement.If $x=2$ in $x+3=5$, then $2+3=5$, which is true, so $x=2$ satisfies the equati...

The Substitution Principle If a variable appears multiple times in an equation, substitute the given value for *every* instance of that variable. To check if a value satisfies an equation, replace the variable with the given number. For example, if checking $x=3$ in $2x + x = 9$, you would write $2(3) + 3 = 9$. Order of Operations (PEMDAS/BODMAS) After substituting, evaluate each side of the equation using the correct order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This ensures you correctly calculate the value of each expression in the equation. For example, in $3(5) - 7$, you multiply $3 imes 5$ first, then subtract 7. The Equality Check After evaluating bot...