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Part 1

Fill in the blanks.

If

cgreater than>​0,

StartAbsoluteValue u EndAbsoluteValueuequals=c

is equivalent to

uequals=​_______

or

uequals=​_______.

Given the problem:

If \( c > 0 \), the equation \( |u| = c \) is equivalent to:

\[
u = \, \boxed{c} \quad \text{or} \quad u = \, \boxed{-c}.
\]

This is because the absolute value equation \( |u| = c \) means that \( u \) can either be \( c \) or \( -c \), since both values have an absolute value of \( c \).

Would you like further details or clarifications? Here are five follow-up questions to explore the topic:

1. What happens if \( c = 0 \) in the equation \( |u| = c \)?
2. How would you solve an equation like \( |u| = c \) if \( c < 0 \)?
3. Can you apply the absolute value concept to inequalities, such as \( |u| < c \)?
4. What is the graphical interpretation of the equation \( |u| = c \) on a number line?
5. How would you solve more complex absolute value equations like \( |2u + 3| = 5 \)?

**Tip**: Absolute value equations often yield two possible solutions. Always consider both the positive and negative possibilities.

If c > 0, |u| = c is equivalent to u = _______ or u = _______.

Discover how to solve the absolute value equation |u| = c, where c > 0. This problem explores the properties of absolute values and linear equations, providing a step-by-step solution. Ideal for students in Grades 6-8.

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