Answer: D) multiply the entire equation by 6, E) x + 90 = 4x, yes
Explanation:
Our 2 choices for the least common denominator are 3 and 6. Our least common denominator is 6 because in order to make a fraction an integer, you multiply the fraction by the number in its denominator (or a multiple of this number, and 6 is a multiple of 3). We will be multiplying the entire equation by 6 to rewrite the equation; if we multiplied it by 3, this is our result:
3(1/6x + 15 = 2/3x) => 1/2x + 45 = 2x
We still have a fraction as a coefficient, when we want all integer coefficients.
Multiplying the original equation by 6 leads to:
6(1/6x + 15 = 2/3x) => x + 90 = 4x
We want to isolate x, so we subtract x from both sides:
x + 90 = 4x
-x -x
90 = 3x
Now, we solve for x:
90/3 = 3x/3
30 = x
We obtained the same result as the original equation.
I hope this helps! :)