Which of the following equations has an infinite number of solutions?

Question

a. 3x – 3 = –4x
b. 2y + 4 – y = 16
c. 7x + 5 = 4x + 5 + 3x
d. 6y – 2 = 2(y – 1)

And please explain how I don't understand. Thanks sooooo much!!!

Answer 1

look at c. Why can't you solve for x, as in the others?

Answer 2

The reason the that C has an infinite number of solutions as opposed to the others is because you essentially have
7x +5 = 7x +5 (because you can add the
4x and 3x to make 7x so any answer will work because it will be the same answer on each side no matter what and the other problems will all end up with X = to something were as C would end up 0=0

Answer 3

a.

3 x – 3 = – 4 x Add 4x to both sides

3 x – 3 + 4 x = – 4 x 4 x

7 x - 3 = 0 Add 3 to bozh sides

7 x - 3 + 3 = 0 + 3

7 x = 3 Divide both sides by 7

x = 3 / 7

ONLY ONE SOLUTION

b.

2 y + 4 – y = 16

y + 4 = 16 Subtracr 4 to both sides

y + 4 - 4 = 16 - 4

y = 12

ONLY ONE SOLUTION

c.

7 x + 5 = 4 x + 5 + 3 x

7 x + 5 = 7 x + 5

THAT IS TRUE FOR ALL VALUES OF x.

INFINITE NUMBER OF SOLUTIONS

d.

6 y – 2 = 2 ( y – 1 ) Divide both sides by 2

3 y - 1 = y - 1 Subtract y to both sides

3 y - y - 1 = - y - 1 - y

2 y - 1 = - 1 Add 1 to both sides

2 y - 1 + 1 = - 1 + 1

2 y = 0 Divide both sides by 2

y = 0

ONLY ONE SOLUTION

CORRECT ANSWER :

c