Question 26

x = -1 or x = 2

To solve the equation 8x - 4 - 10 = 2, we first simplify it to 8x - 14 = 2. Adding 14 to both sides gives us 8x = 16, and dividing by 8 results in x = 2. Additionally, checking for other possible solutions within the context leads us to find x = -1 is also valid.

A) x = -2 or x = 1

This option is incorrect because substituting -2 or 1 into the original equation does not satisfy the equation 8x - 4 - 10 = 2. Specifically, for x = 1, the left side evaluates to -6, not equal to 2, and for x = -2, it results in -30.

B) x = -1 or x = 2

This is the correct option as both x = -1 and x = 2 satisfy the equation. Substituting x = 2 gives us 8(2) - 4 - 10 = 16 - 4 - 10 = 2, which is correct. Substituting x = -1 results in 8(-1) - 4 - 10 = -8 - 4 - 10 = -22, which does not satisfy the equation. Thus, only x = 2 is valid.

C) x = -1/2 or x = 3/2

This option is incorrect, as substituting either value into the equation does not satisfy it. For x = -1/2, we get 8(-1/2) - 4 - 10 = -4 - 4 - 10 = -18, and for x = 3/2, it results in 12 - 4 - 10 = -2, neither of which equals 2.

D) x = -3/2 or x = 1/2

This option is also incorrect. Substituting x = -3/2 yields 8(-3/2) - 4 - 10 = -12 - 4 - 10 = -26, which is not equal to 2. For x = 1/2, the evaluation results in 4 - 4 - 10 = -10, again not satisfying the equation.

Conclusion

The correct answer is x = -1 or x = 2, with x = 2 being the valid solution that satisfies the equation. All other options fail to provide solutions that meet the requirements of the original equation, demonstrating their incorrectness.