For what value of the constant *c* the equation 3(2*x* + *c*) = 6*x* + 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(2*x* + *c*) = 6*x* + 2 + *c* --> 6*x* + 3*c =* 6*x* + 2 + *c.*

Coefficients: The coefficients are same on both sides.

Constants:

Left expression constant is 3*c. *

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.

3*c = *2 + *c * --> 3*c - c = *2 --> 2*c = *2 --> *c *= 1.

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