Question

Complete each equation so that it has the indicated number of solutions

Answer 1

Answer:

No solutions: 3x + 1 = 3x + b, where b ≠ 1

Infinite solutions: 2x - 4 = 2x - 4

Step-by-step explanation:

For an equation to have no solutions, it has to reduce to an equation that's never true. For our given equation, this means we'll need to fill in the blank with some value other than 1. If we pick 2, for instance, we'll get the equation 3x + 1 = 3x + 2, which reduces to 1 = 2, a false statement. No value of x will make the equation true.

To have infinite solutions, on the other hand, we need an equation that is always true. Filling in the blank with 4 here will give us one: 2x - 4 = 2x - 4 reduces to -4 = -4, a statement that is always true.