Question

Test Prep How many solutions does the following equation have? If there is only one solution, find it. 2x+8=2(x+3) Responses one solution, x=2 one solution, x is equal to 2 one solution, x=14 one solution, x is equal to 14 no solution no solution infinitely many solutions infinitely many solutions Skip to navigation

Answer 1

Answer: no solution

Reason

The 2(x+3) on the right hand side distributes to 2x+6

The original equation turns into 2x+8 = 2x+6.

Subtract 2x from both sides to have them cancel out. We're left with the equation of 8 = 6 which is always false. No matter what we replace x with, the original equation is never true.

In terms of a graph, y = 2x+8 and y = 2x+6 are parallel lines that never intersect. We need an intersection point to get a solution.