Absolute Value Expressions and Equations

Expressions involving absolute values are concerned with the measurement of a number's distance from zero on the number line, independent of its direction. On the other hand, absolute value equations are about determining the range of values that satisfy the given equation. The solution process entails separating the absolute value expression and taking into account both the positive and negative potential outcomes.

Simplifying Absolute Value Expressions

Simplify the following absolute value expression: \( |3x - 2| + |2 - 3x| \)

Solving with Absolute Values

Solve the equation \(\left| 5x - 3 \right| = 7\).

Finding the Vertex for the Absolute Value

Find the vertex of the absolute value function \(y = 3|x - 2| + 4\).

Rewriting the Absolute Value as Piecewise

Solve the absolute value equation: \( |2x - 3| = 5 \)