What is the solution of the equation |7x - 9| = 5?

Rationale

-4/7 and 2

To solve the equation |7x - 9| = 5, we consider both scenarios where the expression inside the absolute value can equal 5 or -5. This leads us to two equations: 7x - 9 = 5 and 7x - 9 = -5, which yield the solutions -4/7 and 2.

A (-4/7 only) YOUR ANSWER

This option provides only one solution, -4/7, which is derived from the equation 7x - 9 = -5. However, it neglects the second solution from the equation 7x - 9 = 5, which is necessary to fully solve the absolute value equation.

B (4/7 only) YOUR ANSWER

The solution 4/7 does not arise from either of the equations derived from the absolute value. This choice is incorrect as it does not represent a valid solution to |7x - 9| = 5.

C (2 only) YOUR ANSWER

While 2 is indeed one of the solutions, this option fails to include the other solution, -4/7, obtained from the equation 7x - 9 = -5. Thus, it does not represent the complete solution set.

D (-4/7 and 2) CORRECT

This option correctly identifies both solutions derived from the absolute value equation, making it the complete and accurate answer. It includes all the necessary solutions required to satisfy the equation.

E (4/7 and 2) YOUR ANSWER

This option incorrectly includes 4/7, which is not a solution derived from the absolute value equation. Therefore, while it correctly identifies 2, the presence of 4/7 renders it incorrect.

Conclusion

The equation |7x - 9| = 5 produces two valid solutions: -4/7 and 2, obtained from solving the absolute value conditions. The correct answer, thus, is option D, which encompasses both solutions. Other options either provide incomplete solutions or incorrectly include numbers that do not satisfy the equation.

What is the solution of the equation |7x - 9| = 5?

-4/7 and 2

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