Question

2(12 - y) = 23- (2y - 1) is there a solution for this?

Answer 1

This equation is an identity, all real numbers are solutions.

Explanation:

Simplifying

2(12 + -1y) = 23 + -1(2y + -1)

(12 * 2 + -1y * 2) = 23 + -1(2y + -1)

(24 + -2y) = 23 + -1(2y + -1)

Reorder the terms:

24 + -2y = 23 + -1(-1 + 2y)

24 + -2y = 23 + (-1 * -1 + 2y * -1)

24 + -2y = 23 + (1 + -2y)

Combine like terms: 23 + 1 = 24

24 + -2y = 24 + -2y

Add '-24' to each side of the equation.

24 + -24 + -2y = 24 + -24 + -2y

Combine like terms: 24 + -24 = 0

0 + -2y = 24 + -24 + -2y

-2y = 24 + -24 + -2y

Combine like terms: 24 + -24 = 0

-2y = 0 + -2y

-2y = -2y

Add '2y' to each side of the equation.

-2y + 2y = -2y + 2y

Combine like terms: -2y + 2y = 0

0 = -2y + 2y

Combine like terms: -2y + 2y = 0

0 = 0

Solving

0 = 0

Answer 2

Explanation:

Short Answer: No

2(12 - y) = 23- (2y - 1) Remove the Brackets on both sides

24 - 2y = 23 - 2y + 1 Combine like terms on the right

24 - 2y = 24 - 2y No matter what you do, the 2ys are going to cancel. When they do, the question goes with them.

You get 24 = 24 Which is true but not relevant.

The other answer you could use is there are an infinite number of answers.

Equality will be maintained, but there is no single answer that works.