Question

How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) - 2
zero
one
two
infinitely many

Answer 1

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

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

infinitely many

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