Final answer:
To clear the equation of fractions, multiply each term by the least common multiple (LCM) of the denominators, which is 18. The resulting cleared equation would be 27x - 10x + 36.
Step-by-step explanation:
To clear the equation 3/2x - 5/9x + 2 of fractions, we can find a common denominator and multiply the entire equation by that number. In this equation, the fractions have denominators of 2 and 9. The least common multiple (LCM) of these denominators is 18. Therefore, we would multiply each term of the equation by 18 to clear the fractions.
Here's how it would look in steps:
- Multiply the first term: 18 * (3/2)x which simplifies to 27x.
- Multiply the second term: 18 * (-5/9)x which simplifies to -10x.
- Since the third term does not have a fraction, simply multiply by 18: 18 * 2 which equals 36.
So, we end up with the cleared equation 27x - 10x + 36. Remember, after clearing the fractions, it's often necessary to combine like terms or further simplify the expression if possible.