You have to identify if the following equations have one solution, infinitely many solutions, or no solution.
3u + 40 + 2u = 6u - 30 - u simplify similar terms both sides
5u + 40 = 5u - 30 subtract 5u both sides
40 = - 30
The previous result is an indetermination, hence, the equation does not have solution
2.2z + 3z = 4.5 - 3.2 simplify similar terms
5.2z = 1.3 divide 5.2 both sides
z = 1.3/5.2
z = 0.25
Hence, this equation has one solution
4/5x + 2/3 + 1/5x = x simplify similar terms
5/5 x + 2/3 = x
x + 2/3 = x subtract x both sides
2/3 = 0
The previous result is an indetermination, hence, the equation does not have solution
2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 simplify similar terms both sides
1.3y + 3.2 = 1.3y + 3.2 subtract 1.3y both sides
3.2 = 3.2
The previous result means that the equation has infinite solutions.
2/3x + 2/3 + 1/5x = 2/3x simplify similar terms both sides
19/15 x + 2/3 = 2/3 x subtract 2/3x both sides
3/5 x + 2/3 = 0 subtract 2/3 both sides
3/5 x = - 2/3 multiply by 5/3 both sides
x = -10/9
Hence, the previoues equation has one solution
20 + 4r = 32 - 2r add 2r both sides
20 + 4r + 2r = 32
20 + 6r = 32 subtract 20 both sides
6r = 32 - 20 simplify
6r = 12 divide by 6 both sides
r = 12/6
r = 2
Hence, the previous equation has one solution