Question

Is the equation true, false, or open?. 5x+2=6x+11.

Answer 1

The correct answer is:

True

Explanation:

An equation is false if there is no solution; open if there are an infinite amount of solutions; and true if there is one solution.

To solve this equation, we will gather all of the x's on the same side.  To do this, subtract 6x from each side:

5x+2 = 6x+11

5x+2-6x = 6x+11-6x

-1x+2 = 11

Subtract 2 from each side:

-1x+2-2 = 11-2

-1x = 9

Divide both sides by -1:

-1x/-1 = 9/-1

x = -9

There is one solution, so this is true.

Answer 2

5x + 2 = 6x + 11

5x - 6x = 11 - 2

-x = 9

x = -9

Since there is a solution, hence the equation is true.