In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

Key Concepts

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|, and is always non-negative. For example, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for solving equations that involve it, as it leads to two possible cases based on the definition.

Solving Absolute Value Equations

To solve an absolute value equation, you typically isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case. For instance, if |A| = B, then A = B or A = -B. This method allows you to find all possible solutions that satisfy the original equation.

Checking for Extraneous Solutions

After solving an equation, it is essential to check each solution in the original equation to ensure they are valid. This is particularly important in absolute value equations, as the process of squaring or isolating terms can introduce extraneous solutions that do not satisfy the original equation. Validating solutions helps confirm their correctness.