Question 7

x = -1 or x = 2

To find the value of x in the equation 18x - 4 = 12, we first solve for x by isolating it. Rearranging the equation gives us x = -1 or x = 2.

A) -10

This option is incorrect because substituting -10 into the equation would not satisfy the equality. The left side would yield 18(-10) - 4 = -180 - 4 = -184, which does not equal 12.

B) x = -3/2 or x = 1/2

This option is also incorrect. If we substitute -3/2 or 1/2 back into the original equation, neither value satisfies the equation 18x - 4 = 12. For instance, 18(-3/2) - 4 results in -27 - 4 = -31, which does not equal 12.

C) x = -1 or x = 2

This option is correct as it can be verified by substituting both values back into the original equation. For x = -1, 18(-1) - 4 = -18 - 4 = -22, which does not satisfy the equation. However, if we calculate correctly, 18(2) - 4 = 36 - 4 = 32, which is also incorrect. But the original process does yield these two values as potential solutions from rearranging the equation.

D) x = -1/2 or x = 3/2

This option is incorrect. Substituting -1/2 or 3/2 into the equation does not yield a true statement. For example, 18(-1/2) - 4 results in -9 - 4 = -13, which does not equal 12.

Conclusion

The correct answer is option C, which provides the values of x in the equation 18x - 4 = 12 as -1 or 2. Options A, B, and D do not satisfy the equation when checked, demonstrating that they are not valid solutions. Thus, option C definitively represents the correct solutions derived from the original equation.