Question

How many solutions exist for the given equation?

Answer 1

Answer:

$\Huge \boxed{\mathrm{infinite \ solutions}}$

Step-by-step explanation:

$\sf 12x + 1 = 3(4x + 1) - 2$

Using distributive property.

$\sf 12x + 1 = 12x+3 - 2$

$\sf 12x + 1 = 12x+1$

Subtracting 1 from both sides.

$\sf 12x=12x$

Dividing both sides by 12.

$\sf x=x$

All real numbers are solutions.

There are infinite solutions.

Answer 2

Answer:

infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

Distribute

12x + 1 = 12x + 3 - 2

Combine like terms

12x+1 = 12x +1

Subtract 12x from each side

1 =1

Since this is always true, we have infinite solutions