Determine whether the following system of equations has one solution, no solution, or an infinite number of solutions. Explain your reasoning 3 (x+4) = x+2

One solution, x = - 5.

Step-by-step explanation:

3 (x + 4) = x + 2 Distributing the 3 over the brackets:

3x + 12 = x + 2 Subtract x from both sides and subtract 12 from both sides:

3x - x = 2 - 12 Simplify:

2x = - 10 Divide both sides by 2:

x = - 5.

It has infinite number of solutions because you can put infinite number of values for a given variable: Here, x

For example you can put the value of 6 = x

or 7 = x and etc.

Therefore infinite values so infinite solutions ...