Graphing Modulus Inequalities with Multiple Absolute Values
Solve the inequality \(|2x – 3| + |x + 1| < 5\). Provide a comprehensive description of the x-regions where the inequality holds, and explain how you would graph this solution on a number line.
Intersection of Modulus Functions with Transformations
Consider the functions: \( f(x) = |x – 3| \) \( g(x) = 2 – |x – 4| \) Find the coordinates of the intersection points of the graphs of \( f(x) \) and \( g(x) \).
Part a
Formulate the equation using absolute value notation for the object being exactly d units away from the reference point. Clearly state the two cases that result from this formulation.