Solve each equation and answer if there are infinite solutions, one solution, or no solution. If there is one solution, give the solution.
3(y+2)+2y=7(y-1)+9
4(w+1)-7=3(w-1)+w
To solve the first equation:
3(y+2)+2y=7(y-1)+9
Simplifying both sides of the equation:
3y + 6 + 2y = 7y - 7 + 9
Combining like terms:
5y + 6 = 7y + 2
Subtracting 5y from both sides of the equation:
6 = 2y + 2
Subtracting 2 from both sides of the equation:
4 = 2y
Dividing both sides of the equation by 2:
2 = y
Therefore, the solution to the first equation is y = 2.
To solve the second equation:
4(w+1)-7=3(w-1)+w
Simplifying both sides of the equation:
4w + 4 - 7 = 3w - 3 + w
Combining like terms:
4w - 3 = 4w - 3
Subtracting 4w from both sides of the equation:
-3 = -3
Since -3 is equal to -3, this equation has infinite solutions.