In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For any real number x, the absolute value is always non-negative, meaning |x| ≥ 0. Therefore, an equation like |x| = -6 has no solution, as absolute values cannot equal negative numbers.

Two equations are equivalent if they have the same solution set. In this case, the statement claims that |x| = -6 is equivalent to x = 6 or x = -6. However, since |x| cannot be negative, the original equation has no solutions, making the equivalence false. Understanding equivalence is crucial for validating statements in algebra.

In algebra, determining the truth value of a statement involves verifying if the statement holds under the defined conditions. A false statement can often be corrected by altering its components. In this case, the statement is false because it incorrectly asserts that |x| can equal a negative number, which is impossible. Recognizing true and false statements is essential for logical reasoning in mathematics.