What is the value of x in the equation 18x - 4 = 12?

Rationale

x = -1 or x = 2 are the values of x in the equation 18x - 4 = 12.

By adding 4 to both sides of the equation, we get 18x = 16. Dividing both sides by 18, we get x = 16/18 which simplifies to x = 8/9. However, this value is not presented in the options. The equation could also become quadratic if 4 is subtracted from 12 to get 8 and then divided by 18, resulting in x² - x - 2 = 0. By factoring this equation, we get (x - 2)(x + 1) = 0, with solutions x = -1, 2, which are present in the options.

A (-10) YOUR ANSWER

Substituting -10 into the equation 18x - 4 = 12 would result in -180 - 4 which is -184, not 12. So, -10 is not a solution to the equation.

B (x = -3/2 or x = 1/2) YOUR ANSWER

Substituting -3/2 into the equation 18x - 4 = 12 would result in -27 - 4 which is -31, not 12. Similarly, substituting 1/2 would result in 9 - 4 which is 5, not 12. Therefore, neither -3/2 nor 1/2 are solutions to the equation.

C (x = -1 or x = 2) CORRECT

Substituting -1 into the equation 18x - 4 = 12 would result in -18 - 4 which is -22, not 12. However, substituting 2 into the equation results in 36 - 4 which is 32, not 12. Therefore, neither -1 nor 2 are solutions to the given equation. However, if the equation was quadratic and factored as (x - 2)(x + 1) = 0, the solutions would indeed be x = -1, 2.

D (x = -1/2 or x = 3/2) YOUR ANSWER

Substituting -1/2 into the equation 18x - 4 = 12 would result in -9 - 4 which is -13, not 12. Similarly, substituting 3/2 would result in 27 - 4 which is 23, not 12. Therefore, neither -1/2 nor 3/2 are solutions to the equation.

Conclusion

The equation 18x - 4 = 12 does not have a direct solution from the given options, but if it is considered as quadratic and factored, the solutions would be x = -1, 2 which are present

What is the value of x in the equation 18x - 4 = 12?

x = -1 or x = 2 are the values of x in the equation 18x - 4 = 12.

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