Solve equations: word problems

Learning Objectives Identify the unknown quantity in a word problem and represent it with a variable. Translate verbal phrases and sentences into one-variable algebraic expressions and equations. Set up a one-variable linear equation that accurately models a given word problem. Solve one-variable linear equations using inverse operations. Interpret the solution of an equation in the context of the original word problem. Check the reasonableness of their solution by substituting it back into the original problem. Ever wonder how math helps us solve everyday puzzles? 🕵️‍♀️ From sharing candy fairly to figuring out how much money you need for a new game, word problems are everywhere! In this lesson, you'll learn how to turn tricky word problems into simple one-variable eq...

TermDefinitionExample Word ProblemA mathematical problem presented in a narrative or descriptive form, requiring you to extract information and set up an equation to find a solution.Sarah has 5 apples, and her friend gives her 3 more. How many apples does Sarah have now? VariableA symbol, usually a letter (like 'x' or 'n'), that represents an unknown number or quantity in an equation.In the problem 'A number plus 7 is 15', we can let 'x' be the unknown number, so the equation is x + 7 = 15. EquationA mathematical statement that shows two expressions are equal, typically containing an equals sign (=).3x + 5 = 14 is an equation where '3x + 5' is equal to '14'. Algebraic ExpressionA mathematical phrase that can contain numbers, vari...

The 5-Step Word Problem Solving Strategy 1. Read the problem carefully. 2. Define a variable. 3. Write an equation. 4. Solve the equation. 5. Check your answer. This systematic approach helps you break down any word problem into manageable parts, ensuring you understand the problem, set it up correctly, and verify your solution. Inverse Operations for One-Variable Equations To solve for a variable, perform the inverse operation on both sides of the equation to isolate the variable. * If a number is added to the variable, subtract it from both sides. (e.g., $x + a = b \implies x = b - a$) * If a number is subtracted from the variable, add it to both sides. (e.g., $x - a = b \implies x = b + a$) * If a variable is multiplied by a number, divide both sides by that number....