Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For any real number x, |x| is always non-negative, meaning it can never be less than zero. This property is crucial for solving equations involving absolute values, as it dictates the possible values that satisfy the equation.
Recommended video:
Parabolas as Conic Sections Example 1
Solving Absolute Value Equations
To solve an equation involving absolute values, such as |A| = B, we consider two cases: A = B and A = -B. This is because the absolute value of a number can be equal to a positive number in two scenarios: the number itself or its negative counterpart. In the case of |A| = 0, the only solution is A = 0, as absolute values cannot be negative.
Recommended video:
Solving Logarithmic Equations
Zero as a Solution
In the context of equations, zero is a unique solution that indicates the absence of a quantity. When solving equations like |8x + 5| = 0, we find that the expression inside the absolute value must equal zero for the equation to hold true. This leads to a straightforward solution process, as it simplifies to solving a linear equation.
Recommended video:
Finding Zeros & Their Multiplicity