Answer: x in its simplest form is x = 20/3.
Explanation:
1. Begin by distributing the fraction 1/8 to the terms inside the parentheses: (6x - 24).
This gives us: 2 = (1/8) * 6x - (1/8) * 24.
2. Simplify the equation by multiplying. (1/8) * 6x equals (6/8)x, which can be simplified to (3/4)x.
And (1/8) * 24 equals (24/8), which is 3.
3. Now, the equation becomes: 2 = (3/4)x - 3.
4. To eliminate the fraction, we can multiply both sides of the equation by the reciprocal of the fraction's denominator, which is 4/1. This gives us:
2 * (4/1) = (3/4)x * (4/1) - 3 * (4/1).
5. Simplifying further, 2 * 4 equals 8, and (3/4)x * 4 equals 3x.
The equation becomes: 8 = 3x - 12.
6. To isolate the variable, add 12 to both sides of the equation: 8 + 12 = 3x - 12 + 12.
7. This simplifies to: 20 = 3x.
8. Finally, divide both sides of the equation by 3 to solve for x: 20/3 = (3x)/3.
9. The equation further simplifies to: 20/3 = x