Tell whether the equation is one solution no solution or an infinite

Question

2(x+3)=2x+6
A value of x that makes the equation true is ________,which when substituted into the equation and simplified makes the equation turn into.____=_____
A value of x that makes the equation false is_____, which when substituted into the equation and simplified makes the equation turn into ______=_____

Answer 1

To determine the nature of the equation 2(x+3)=2x+6, we will simplify and solve the equation step by step.

Expanding both sides of the equation:
2x + 6 = 2x + 6

Subtracting 2x from both sides of the equation:
6 = 6

Since the variable x does not appear in the simplified equation, any value of x will make the equation true. Therefore, the given equation has an infinite number of solutions.

A value of x that makes the equation true is any real number; when substituted into the equation and simplified, it remains true.

A value of x that makes the equation false does not exist, as the equation is always true for any value of x.