Final answer:
To rewrite the equation 7 + (5/9)x = 2/3 without fractions, multiply all terms by the least common multiple of the denominators (9), resulting in 5x = -57.
Step-by-step explanation:
To rewrite the equation 7 + (5/9)x = 2/3 without fractions, we first want to eliminate the denominators. Multiplication and division are inverse operations, so to remove a fraction we can multiply by its denominator. To clear the fraction (5/9)x, we would multiply each term by 9, and to clear the fraction 2/3, we would need to multiply each term by 3. When we do this, we get:
9 * 7 + 9 * (5/9)x = 9 * (2/3)
This simplifies to:
63 + 5x = 6
Now we need to get the 'x' term by itself, so we subtract 63 from both sides:
5x = 6 - 63
5x = -57
Finally, we divide by 5 to solve for x:
x = -57/5
So the fraction-free version of the equation is 5x = -57.