Question 24

-4/7 and 2

The solutions to the equation |7x - 9| = 5 are -4/7 and 2, as both values satisfy the condition set by the absolute value equation.

A) -4/7 only

This option is incorrect because it suggests that -4/7 is the sole solution. However, while -4/7 does satisfy the equation, it ignores the second valid solution, which is 2.

B) 4/7 only

This option is also incorrect. Although 4/7 is a potential candidate when solving the equation, it does not satisfy the original absolute value equation. Therefore, it cannot be considered a valid solution.

C) 2 only

This option is incorrect because it only identifies 2 as a solution, neglecting the fact that -4/7 is also a valid solution. Both values are necessary to fully address the equation.

D) -4/7 and 2

This option is correct as it encompasses both solutions derived from the equation. To solve |7x - 9| = 5, we consider two cases: 7x - 9 = 5 and 7x - 9 = -5, leading to the solutions of -4/7 and 2.

E) 4/7 and 2

This option is incorrect. While it correctly includes 2, it mistakenly identifies 4/7 as a solution rather than -4/7, which is the actual solution for the equation.

Conclusion

The correct answer, -4/7 and 2, encompasses both valid solutions to the equation |7x - 9| = 5. All other options either omit one of the solutions or include incorrect values, failing to accurately represent the outcomes of the absolute value equation. Thus, option D is the definitive solution.