Question

Using the expression X +3, write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions. Explain.

Answer 1

1. Equation with One Solution: X + 3 = 10
2. Equation with No Solution: X + 3 = 5
3. Equation with Infinitely Many Solutions: X + 3 = X + 3

Explanation:

1. In this equation, there's a unique solution. Subtracting 3 from both sides gives X = 7. So, the value of X that satisfies this equation is 7
2. In this equation, there is no value of X that can satisfy it. If we subtract 3 from both sides, we get X = 2 But since the original equation stated X + 3 = 5, it's clear that there's a contradiction. So, there is no solution for this equation.
3. In this equation, any value of X that you substitute will satisfy it. If you subtract X from both sides, you get 3 = 3 which is always true regardless of the value of X. This means that there are infinitely many values of X that can make this equation true.

Summary:

1. X + 3 = 10 has one solution (x =7)
2. x + 3 = 5 has no solution.
3. x + 3 = x + 3 has infinitely many solutions