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Solving Two Step Linear Inequalities

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Solving Two Step Linear Inequalities

Study Guide

Key Definition

A two-step linear inequality is an inequality that requires two inverse operations to solve. For example, $2x + 1 < 7$.

Important Notes

To solve $2x + 1 < 7$, first subtract 1 then divide by 2.
When dividing by a negative, reverse the inequality sign.
Inequality signs include $<$, $>$, $\leq$, $\geq$.
Use inverse operations to isolate the variable.
Check solutions by substituting back into the original inequality.

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 inequalities uses the same principles as solving equations, but the inequality sign reverses when multiplying or dividing by a negative number.

Remember

Always perform the same operation on both sides of the inequality to maintain balance.

Quick Reference

Inverse Operations:Addition/Subtraction and Multiplication/Division

Understanding Solving Two Step Linear Inequalities

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

For example, to solve $2x + 1 < 7$: first subtract 1 from both sides to get $2x < 6$, then divide both sides by 2 to get $x < 3$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $2x + 1 < 7$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $2x + 3 < 11$ dollars to spend. How much can you spend per item?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $-4x + 5 \geq 1$, what is the range for $x$?

Challenge Quiz

Single Choice Quiz

Advanced

Solve $5x - 3 \geq 2x + 6$

Recap

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Review key concepts and takeaways