Inequalities & Absolute Value 🌱

Interactive Lesson • Practice Problems • Speed Quiz

What Are They?

  **Inequalities** are mathematical sentences that compare two values using symbols like `>` (greater than), `<` (less than), `≥` (greater than or equal to), and `≤` (less than or equal to). The solution to an inequality is a range of numbers.

  **Absolute value** represents the distance of a number from zero on the number line. It's always a positive value, denoted by two vertical bars: $|x|$. For example, $|-5| = 5$ and $|5| = 5$.

  To solve absolute value equations like $|ax+b|=c$, you must consider two cases: $ax+b=c$ and $ax+b=-c$.

 
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Video: Solving Absolute Value Equations 🎬

This video will show you how to solve an absolute value equation by considering two cases.

 
 
 

Practice Problems

Solve the following problems and check your answers.

 
   
1) Solve the inequality:
$$2x + 1 > 5$$
   

Answer:

   
   
 
 
   
2) Solve the absolute value:
$$|x-3| = 4$$
   

Answer:

   
   
 
 
   
3) Evaluate:
$$|-15|$$
   

Value:

   
   
 
 
   
4) Solve the inequality:
$$3x - 5 \le 10$$
   

Value:

   
   
 

⚡ Speed Quiz

       
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