实数的绝对值

Introduction: From Distance to Absolute Value

Definition of Absolute Value

Which of the following statements about $|x|$ is correct?

Multiplicativity

What is $|(-2)\cdot 5|$?

Triangle Inequality

What is the condition for equality $|a+b|=|a|+|b|$?

Range of the Absolute Value of a Sum

When $|a|=3$, $|b|=4$, and $a,b$ have opposite signs, what is the value of $|a+b|$?

Worked Example: Removing Absolute Value by Intervals

Solve the equation $|x-3|=5$. Write all real solutions separated by semicolons (no spaces).

Solve the inequality $|x-2|<3$. Write the solution set as an open interval (no spaces).

Find the minimum of $|x-1|+|x-4|$. Enter an integer.

What are the triangle inequality and its corollary? What are the equality conditions?

Explain in your own words: what are the geometric meanings of $|x-a|=b$ and $|x-a|<b$ respectively? Why is there no solution when $b<0$?

Comprehensive Check

Correcting Common Errors and Lesson Summary