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Word Problems Involving Two-Step Linear Equations

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Word Problems Involving Two-Step Linear Equations

Study Guide

Key Definition

In a two-step linear equation, you perform two inverse operations in reverse order of the original operations to isolate the variable. For example, in $ax + b = c$, first subtract $b$ then divide by $a$.

Important Notes

Always perform operations in the correct order: reverse of PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)
Check your solution by substituting back into the original equation
Be careful with negative numbers and subtraction
Use keywords in word problems to determine operations
Identify the variable and what it represents in the problem

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

By reversing the order of operations—undoing addition or subtraction before multiplication or division—you systematically isolate the variable. Maintaining equality at each step ensures an accurate solution.

Remember

Always reverse the order of operations: undo addition/subtraction first, then multiplication/division. Verify your answer by plugging it back into the original equation.

Quick Reference

Two-Step Equation:$ax + b = c$

Understanding Word Problems Involving Two-Step Linear Equations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In a two-step linear equation of the form $ax + b = c$, first subtract $b$ from both sides to get $ax = c - b$, then divide by $a$ to solve for $x$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $2x + 3 = 7$. What is $x$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $3$ dollars and earn $2$ dollars for each chore you do. How many chores must you complete so that you have $7$ dollars in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A cell phone plan has a $$50$ monthly fee plus $$2$ per minute of call time. If you spend $$100$ in a month, how many minutes did you talk? Here $x$ is the number of minutes talked.

Challenge Quiz

Single Choice Quiz

Advanced

Solve the equation $3x - 4 = 2x + 5$. What is $x$?

Recap

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Review key concepts and takeaways