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Solving Multi-Step Linear Equations

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Solving Multi-Step Linear Equations

Study Guide

Key Definition

A multi-step linear equation requires using inverse operations to isolate the variable, often involving combining like terms and undoing addition or subtraction.

Important Notes

Use inverse operations to solve equations.
Combine like terms for simplification.
Work backwards to isolate the variable.
Check your solution by substituting back into the equation.
Remember the Multiplicative Identity: $1·x = x$

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

$=$ represents equality

Use consistent notation: italicize variables, use proper symbols for operations, and label both sides of the equation clearly.

Why It Works

Solving multi-step equations works by systematically reversing operations to isolate the variable, ensuring the equation remains balanced.

Remember

Keep track of your operations and always perform the same operation on both sides of the equation.

Quick Reference

Combining Like Terms:$ax + bx = (a+b)x$

Understanding Solving Multi-Step Linear Equations

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To solve $x + 5 = 10$, subtract 5 from both sides: $x = 10 - 5$. Therefore, $x = 5$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve for $x$: $3x + 4 = 10$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Write and solve an equation to find your original amount if you spent $\$5$ on snacks and have $\$20$ left.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the equation $2(x + 3) = 8$. What is $x$?

Challenge Quiz

Single Choice Quiz

Advanced

Solve for $x$: $4x - 7 = 2x + 5$

Recap

Watch & Learn

Review key concepts and takeaways