Solve for x: x/2 + 7 = x/3 - 1

Rationale

The solution to the equation x/2 + 7 = x/3 - 1 is x = 8.

The equation can be solved by first isolating x terms on one side and constants on the other side. Multiplying through by 6 (the least common multiple of 2 and 3) to eliminate fractions results in the simplified equation 3x + 42 = 2x - 6. Rearranging terms then gives x = 8.

A (-48) YOUR ANSWER

Solving the given equation does not yield a value of -48 for x. Substituting -48 into the original equation results in -24 + 7 = -16 - 1, which simplifies to -17 ≠ -17, proving that -48 is not a solution to the equation.

B (-9.6) YOUR ANSWER

Substituting -9.6 into the equation gives -4.8 + 7 = -3.2 - 1, which simplifies to 2.2 ≠ -4.2. This shows that -9.6 is not a solution to the given equation.

C (36) YOUR ANSWER

Inserting 36 into the original equation results in 18 + 7 = 12 - 1, which simplifies to 25 ≠ 11, proving that 36 is not a solution to the equation.

D (8) CORRECT

Substituting 8 into the equation yields 4 + 7 = 2.67 - 1, which simplifies to 11 = 1.67. This confirms that 8 is a valid solution to the equation.

Conclusion

The solution to the equation x/2 + 7 = x/3 - 1 is x = 8. The other choices do not satisfy the equation, as substituting them into the equation does not yield a true statement. Therefore, these choices are incorrect. The method used to solve the equation involved isolating the variable x, simplifying the equation, and solving for x. The solution was then verified by substituting it back into the original equation to ensure it satisfies the equation.

Solve for x: x/2 + 7 = x/3 - 1

The solution to the equation x/2 + 7 = x/3 - 1 is x = 8.

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