For what value of the constant c the equation 3(2x + c) = 6x + 2 + c has infinitely many solutions?
Maps to Category 13 of the book.
Answer posted on 07/18/2021: Answer is 1.
For the equation to have infinitely many solutions, expressions on both sides of the equation must be equal. The coefficient of x in both the expressions must be same and the constant in both the expressions must be same.
Simplify the left expression and equate the coefficients and constants.
3(2x + c) = 6x + 2 + c --> 6x + 3c = 6x + 2 + c.
Coefficients: The coefficients are same on both sides.
Left expression constant is 3c.
Right expression constant is 2 + c.
Equate and determine the value of c that makes both sides equal. We can see that if c is 1, then constant on both the sides will equal to 3. Hence, c = 1. See calculation below.
3c = 2 + c --> 3c - c = 2 --> 2c = 2 --> c = 1.