If (2x - 4) / 7 = 6, what is the value of x?

Rationale

The value of x is 19.

To solve the equation (2x - 4) / 7 = 6, we can first multiply both sides by 7, yielding 2x - 4 = 42. Adding 4 to both sides gives 2x = 46, and dividing by 2 results in x = 23. However, it seems there is a mistake in the provided answer key; the correct answer should be 23, not 19. Let's clarify the incorrect options.

A (5) YOUR ANSWER

Substituting x = 5 into the original equation gives (2(5) - 4) / 7 = (10 - 4) / 7 = 6 / 7, which does not equal 6. Therefore, x = 5 is not a solution to the equation.

B (8) YOUR ANSWER

If we substitute x = 8, we find (2(8) - 4) / 7 = (16 - 4) / 7 = 12 / 7, which also does not equal 6. Hence, x = 8 is incorrect.

C (19) CORRECT

Plugging x = 19 into the equation gives (2(19) - 4) / 7 = (38 - 4) / 7 = 34 / 7, which does not equal 6. Thus, x = 19 is not the solution.

D (23) YOUR ANSWER

When substituting x = 23, we have (2(23) - 4) / 7 = (46 - 4) / 7 = 42 / 7 = 6. This shows that x = 23 is indeed the correct answer to the equation.

E (35) YOUR ANSWER

Lastly, substituting x = 35 results in (2(35) - 4) / 7 = (70 - 4) / 7 = 66 / 7, which does not equal 6. Therefore, x = 35 is also incorrect.

Conclusion

To find the value of x in the equation (2x - 4) / 7 = 6, we correctly identify that x = 23 is the valid solution. The other choices do not satisfy the equation when substituted back, confirming that they are not the correct values.

If (2x - 4) / 7 = 6, what is the value of x?

The value of x is 19.

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