Question

For each equation find if it has infinite solutions no solutions or one solution. If it has one solution give the solution.

2(u+2)-u=3(u-1)+9

4(w+1)-w=3(w-1)+7

Answer 1

To solve the first equation, we will simplify both sides:

2(u + 2) - u = 3(u - 1) + 9
2u + 4 - u = 3u - 3 + 9
u + 4 = 3u + 6

Next, we will move all the variables to one side of the equation and the constants to the other side:

u - 3u = 6 - 4
-2u = 2

Now, we will isolate u by dividing both sides by -2:

u = 2/-2
u = -1

Therefore, the first equation has one solution: u = -1.

For the second equation:

4(w + 1) - w = 3(w - 1) + 7
4w + 4 - w = 3w - 3 + 7
3w + 4 = 3w + 4

In this case, we notice that the variables cancel out, and we are left with a true statement: 4 = 4. This means that the equation is always true, regardless of the value of w.

Therefore, the second equation has infinite solutions.