Question

Determine whether the equation has one solution, no solution, or infinite solutions.

Explain your reasoning.
9x + 2 = -4(x + 6)

Answer 1

The equation has 1 solution.

Explanation:

Because you don't get the same answer on both sides, this equation does not have infinately many solutions. Because you don't get an invalid answer, such as 1 = 0, this equation doesn't have one solution. When you solve this equation, you'd get something similar to this

9x-2 = -4x-24 (distributive property)

13x-2=-24 (combine like terms)

13x=-22 (additive property of inversion)

x = -22/13

which is a valid, real-world solution.