Question 15

x = 8

To solve for x in the equation x/2 + 7 = x/3 - 1, we find that x equals 8.

A) -48

Option A is incorrect because substituting -48 into the original equation does not satisfy the equality. When calculated, the left side yields a value that does not equal the right side, thus confirming that -48 is not a solution.

B) -9.6

Option B is incorrect as well. If -9.6 is substituted into the equation, the left and right sides will not equate, indicating that this value is not a viable solution for the equation.

C) 36

Option C is incorrect because substituting 36 into the equation does not yield a true statement. The resulting calculations demonstrate that the left and right sides are unequal, disqualifying 36 as a solution.

D) 8

Option D is correct. Substituting 8 back into the original equation confirms the equality: (8/2) + 7 equals (8/3) - 1. Both sides simplify to the same value, validating that 8 is indeed the correct solution.

Conclusion

The solution x = 8 is confirmed as correct through substitution into the original equation, producing equivalent results on both sides. All other options fail to satisfy the equation, demonstrating their inaccuracy in solving for x in this context. Thus, 8 is definitively the only correct answer.