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Word Problems Involving One-Step Linear Equations

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Word Problems Involving One-Step Linear Equations

Study Guide

Key Definition

A one-step linear equation can be solved by performing a single operation on both sides of the equation to isolate the variable.

Important Notes

A linear equation involves terms with variables raised to the power of $1$.
Look for keywords like 'sum', 'difference', 'product', and 'quotient' to decide the operation.
Always verify the solution by substituting it back into the original equation.
Use inverse operations to solve the equation.
Drawing diagrams or using charts can help understand the problem better.

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

Solving one-step linear equations involves using inverse operations to maintain equality and isolate the variable on one side.

Remember

Use inverse operations like addition/subtraction or multiplication/division to isolate variables.

Quick Reference

Addition:$x + a = b \Rightarrow x = b - a$

Subtraction:$x - a = b \Rightarrow x = b + a$

Multiplication:$ax = b \Rightarrow x = \frac{b}{a}$

Division:$\frac{x}{a} = b \Rightarrow x = a \times b, \;a \neq 0$

Understanding <a href="word-problems">Word Problems</a> Involving One-Step Linear Equations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To solve equations of the form x + a = b, subtract a from both sides. For example, if x + 3 = 8, then x = 8 - 3 = 5.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve for $x$ if $x + 5 = 12$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $10$ candies and give $x$ candies to your friend. If you have $4$ candies left, find $x$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A book costs $\frac{x}{2}$ dollars, and it sold for $10$ dollars. Find the original price $x$.

Challenge Quiz

Single Choice Quiz

Advanced

Solve for $x$ if $5x = 35$

Recap

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Review key concepts and takeaways