Final answer:
To solve for the value of m in the equation 6(3-2x)-3=mx+18, we simplify the left side and find that m must be equal to -12, which is not among the provided options. Therefore, none of the options are correct but -15 is closest to the correct value.
Step-by-step explanation:
To find the value of m that makes the equation 6(3-2x)-3=mx+18 true for any value of x, we first need to simplify the left side of the equation by distributing the 6 and then combine like terms. We perform the following operations:
- 6 × 3 = 18
- 6 × (-2x) = -12x
- 18 - 3 = 15
After simplification, the left side of the equation becomes -12x + 15. Therefore, the equation can be written as -12x + 15 = mx + 18.
The value of m has to equal the coefficient of the x on the left side for the equation to be true for any x. Thus, m = -12. Since -12 is not one of the provided options (A) -5, (B) 5, (C) -15, (D) 15, it seems there might be a typo in the options provided.
If we are to choose from the given options, none of them are correct. However, in the spirit of the question, if the equation is supposed to represent a line, the choice that approaches the actual slope is (C) -15.