Solve the equation absolute value of 2x - 3 equals 7.

1. The absolute value is already alone on the left, so no isolating is needed. 2. The expression inside can be 7 units from zero in either direction. 3. Write the two equivalent equations: 2x minus 3 equals 7, and 2x minus 3 equals negative 7. 4. From the first, 2x equals 10, so x is 5. 5. From the second, 2x equals negative 4, so x is negative 2. 6. Checking x equal to 5 gives the absolute value of 7, and x equal to negative 2 gives the absolute value of negative 7, both equal to 7. 7. Answering 5 or negative 5 flips the sign of the answer rather than of the expression inside. 8. Answering 2 or negative 2 solves only for the second case and mislabels it. 9. Answering 5 or 2 keeps two positive roots and misses the negative branch entirely. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.7 Solve Absolute Value Inequalities_