Determine the missing values that would make this equation have infinite amount of solutions

Question

2(6x+7)=3x+?=∆

Answer 1

To have an infinite amount of solutions, the equation must be true for any value of x.

To ensure this, we need to have the equation simplify to an identity.

Starting with the given equation:
2(6x + 7) = 3x + ∆

Expanding the equation:
12x + 14 = 3x + ∆

Simplifying by subtracting 3x from both sides:
9x + 14 = ∆

To make this equation have an infinite amount of solutions, ∆ must be equal to 9x + 14.

Therefore, the missing value that would make the equation have an infinite amount of solutions is ∆ = 9x + 14.