Final answer:
The equation 3(5+2x) = (-x+15) simplifies to 0 = 0, indicating that there are infinitely many solutions for x, and any real number for x will satisfy the equation.
Step-by-step explanation:
To solve for x in the equation 3(5+2x) = (-x+15), we first need to expand and simplify both sides of the equation. By distributing the 3 on the left side, we get:
3 × 5 + 3 × 2x = 15 + 6x
On the right side, the equation is already simplified to -x + 15.
Now we have:
15 + 6x = -x + 15
Next, we bring the x terms to one side and the constant terms to the other side by adding x to both sides and subtracting 15 from both sides:
15 + 6x + x = -x + 15 + x
15 - 15 + 6x + x = 0 + 7x
This simplifies to:
6x + x = 7x
Since we now have 7x on both sides, we see that the equation simplifies to 0 = 0, which indicates that there are infinitely many solutions, meaning any real number for x will satisfy the equation.