Solve the following equation for x. 6x - 5 = 10x + 15

Rationale

x = -5

To solve the equation 6x - 5 = 10x + 15, we can rearrange the terms to isolate x, ultimately finding that x equals -5.

A (x = -5) CORRECT

This choice is the correct solution derived from rearranging the original equation. By moving all x terms to one side and constants to the other, we find that x equals -5, confirmed by substituting back into the original equation.

B (x = 1/5) YOUR ANSWER

This option suggests that x equals 1/5. However, substituting 1/5 back into the original equation results in an incorrect statement: 6(1/5) - 5 does not equal 10(1/5) + 15. Thus, this choice does not satisfy the equation.

C (x = -1/5) YOUR ANSWER

Choosing x = -1/5 also leads to a false statement when substituted back into the original equation. The left side would yield a negative result significantly different from the right side, which fails to balance the equation.

D (x = 5) YOUR ANSWER

This selection indicates that x equals 5. However, substituting 5 into the original equation produces unequal values on both sides, thus confirming that it is not a valid solution to the equation.

Conclusion

The process of solving the equation 6x - 5 = 10x + 15 leads us to find that x equals -5. This solution satisfies the equation, while all other choices do not hold true upon substitution, emphasizing the importance of correctly isolating the variable to determine valid solutions in algebraic equations.

Solve the following equation for x. 6x - 5 = 10x + 15

x = -5

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