How many solutions does 2 (3x+5) = 2 (2x-3) + 2x have

no solutions

Step-by-step explanation:

2 (3x+5) = 2 (2x-3) + 2x

Distribute

6x+10 = 4x - 6 + 2x

Combine like terms

6x+10 = 6x-6

Subtract 6x from each side

6x-6x+10 = 6x-6x-6

10 = - 6

This is never true so there are no solutions

Steps to solve:

2 (3x + 5) = 2 (2x - 3) + 2x

~Distributive Property

(2 * 3x) + (2 * 5) = (2 * 2x) + (2 * - 3) + 2x

~Simplify

6x + 10 = 4x + - 6 + 2x

~Combine Like Terms

6x + 10 = 6x - 6

Subtract 6x to both sides

6x - 6x + 10 = 6x - 6x - 6

~Simplify

10 ≠ - 6

This means that there is no solution.

Best of Luck!