Question

He equations created must be different from any on this practice.

A. Write an equation that has one solution using the variable x. Explain your reasoning.
B. Write an equation that has no solution using the variable y. Explain your reasoning.
C. Write an equation that has infinitely many solutions using the variable x. Explain your reasoning.
a) x + 3 = 7
b) 2y - 5 = 2y
c) 4x - 2 = 2(2x - 1)
d) x = x

Answer 1

An equation that has one solution is x + 3 = 7. An equation with no solution is 2y - 5 = 2y. An equation with infinitely many solutions is 4x - 2 = 2(2x - 1).

Step-by-step explanation:

An equation that has one solution can be written as:

x + 3 = 7

This equation has one solution because when we solve for x, we find that x is equal to 4. Substituting 4 back into the equation gives us 4 + 3 = 7, which is true.

An equation that has no solution can be written as:

2y - 5 = 2y

In this equation, the variable y cancels out, leaving us with the false statement -5 = 0. Since this statement is not true, there is no value of y that would satisfy the equation, hence no solution exists.

An equation that has infinitely many solutions can be written as:

4x - 2 = 2(2x - 1)

When we simplify this equation, we get 4x - 2 = 4x - 2, which means that both sides of the equation are equal. This implies that no matter what value we choose for x, the equation will always be true. Therefore, this equation has infinitely many solutions.