Question

Which equations have infinitely many solutions?
5x - 1 = 5x + 1
3x - 1 = 1 - 3x
7x - 2 = 2x - 7
4(x - 1) = 4x - 4
3x + 6 = 3(x + 2)
3(x - 4) = 4(x - 3)

Answer 1

Answer:

4(x - 1) = 4x - 4

3x + 6 = 3(x + 2)

Step-by-step explanation:

The first equation is

$5x - 1 = 5x + 1$

We simplify to get;

$- 1 = 1$

This is not true, therefore this equation has no solution.

The second equation is

$3x - 1 = 1 - 3x$

Combine like terms:

$3x + 3x = 1 + 1$

$6x = 2$

$x = \frac{1}{3}$

This has a unique solution.

The 3rd equation is

$7x - 2 = 2x - 7$

Group similar terms:

$7x - 2x = 7 + 2 \\ 5x = 9 \\ x = \frac{9}{5}$

The 4th equation is :

$4(x - 1) = 4x - 4$

$4x - 4= 4x - 4 \\ x = x$

This is always true. The equation has infinite solution.

The 5th equation is:

$3x + 6 = 3(x + 2) \\ 3x + 6 = 3x + 6 \\ x = x$

This also has infinite solution

The 6th equation is

$3(x - 4) = 4(x - 3) \\ 3x - 12 = 4x - 12 \\ 3x - 4x = - 12 + 12 \\ x = 0$

It has a unique solution.