What is the solution of the equation |7x - 9| = 5?
4/7 and 2 are the solutions of the equation |7x - 9| = 5.
To solve the equation, we consider the definition of absolute value, which leads to two separate equations: 7x - 9 = 5 and 7x - 9 = -5. Solving these gives us the solutions x = 2 and x = 4/7.
This choice includes only one of the solutions derived from the absolute value equation. While 4/7 is indeed a solution, it does not account for the second solution, which is x = 2. Thus, this option is incomplete.
Similar to option A, this choice also states only one solution, 4/7. Again, it neglects the other valid solution of 2, making it an insufficient answer to the question.
This option acknowledges one of the solutions but ignores 4/7. Therefore, it fails to represent the complete set of solutions to the equation, which consists of both x = 2 and x = 4/7.
This choice correctly lists both solutions derived from the equation. However, it is presented as an alternative interpretation rather than the correct answer designation, failing to emphasize that it is not the only correct format since options E and D are identical.
This option correctly states both solutions obtained from the absolute value equation. It encapsulates the complete set of solutions, demonstrating a thorough understanding of the problem's requirements.
The equation |7x - 9| = 5 yields two valid solutions: 4/7 and 2. While several options provided incomplete or insufficient answers, option E effectively captures both solutions, confirming its correctness. Understanding the principles of absolute value equations is crucial for identifying all possible solutions.
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