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Solving One-Step Linear Inequalities

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Solving One-Step Linear Inequalities

Study Guide

Key Definition

Inequalities are mathematical sentences comparing two quantities that are not equal. Symbols include $\neq$, $<$, $>$, $\leq$, and $\geq$.

Important Notes

Use inverse operations to solve one-step inequalities.
When multiplying or dividing by a negative number, reverse the inequality sign.
Check your solution by substituting back into the original inequality.
Graphing inequalities involves shading the number line.
Inequalities express a range of possible solutions.

Mathematical Notation

$\neq$ means not equal to

$<$ means less than

$>$ means greater than

$\leq$ means less than or equal to

$\geq$ means greater than or equal to

Remember to use proper notation when solving problems

Why It Works

Using inverse operations maintains the balance of the inequality, allowing you to isolate the variable correctly.

Remember

Always reverse the inequality sign when multiplying or dividing both sides by a negative number.

Quick Reference

Inverse Operation:$+$ becomes $-$, $-$ becomes $+$, $\times$ becomes $\div$, and $\div$ becomes $\times$

Understanding Solving One-Step Linear Inequalities

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $basic formulas$ such as $n + 8 < 10$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $n + 8 < 10$. What is $n$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A teenager wants to buy a game that costs less than $\$50$. If they have $\$10$, how much more do they need?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $-3y \geq 15$, find $y$.

Challenge Quiz

Single Choice Quiz

Advanced

Solve the inequality $4x - 7 > 5$. What is $x$?

Recap

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Review key concepts and takeaways