Question

Saskia is solving an equation in one variable and gets the equivalent equation 3=3. Assuming her work is correct, what can she conclude about the original equation?

Answer 1

When Saskia gets the equivalent equation 3=3, it means that the original equation had no variable and has infinitely many solutions.

Step-by-step explanation:

When Saskia gets the equivalent equation 3=3, it means that the original equation had no variable. In other words, the original equation is an identity, where any value of the variable would make the equation true. For example, if the original equation was 2 + 1 = 3, then no matter what value the variable takes, the equation will still be true. So Saskia can conclude that the original equation has infinitely many solutions.

Answer 2

The second option is correct. There are infinitely many solutions.

Step-by-step explanation:

Let's use the equation x + 3 = x + 3

We can simplify this two ways: x = x, or 3 = 3

We can use any value of x so that both sides are equivalent to each other.

For example:

• x + 3 = x + 3
• 2 + 3 = 2 + 3
• 5 = 5

or

• x + 3 = x + 3
• -3 + 3 = -3 + 3
• 0 = 0

As you can see, both sides of the equations are always the same with any value of x.

-Chetan K