True or False Equations

In math, we often need to act like detectives to figure out if a number sentence is true (right) or false (wrong). To do this, we have to look closely at the equal sign!

The Magic of the Equal Sign

The equal sign ($=$) doesn't just mean "here comes the answer." It actually means "is the same amount as."

Imagine a balance scale. For the scale to be perfectly balanced, both sides must weigh exactly the same. If they do, the equation is true. If they don't, the equation is false.

Finding True Equations

An equation is true if both sides of the equal sign equal the exact same number.

Let's look at this equation: $3 + 4 = 7$

To check if it is true, solve the math on the left side:

• $3 + 4 = 7$

Now look at the right side. It is also $7$. Since $7$ is the same as $7$, the equation is true!

Spotting False Equations

An equation is false if the two sides do not match.

Let's look at this equation: $10 - 3 = 8$

To check it, solve the left side first:

• $10 - 3 = 7$

Now compare it to the right side, which is $8$. Does $7$ equal $8$? No! Because the amounts are different, this equation is false.

Equations with Math on Both Sides

Sometimes, you will see addition or subtraction on both sides of the equal sign. Don't worry—just solve one side at a time!

Is this equation true or false? $5 + 2 = 3 + 4$

1. Solve the left side: $5 + 2 = 7$
2. Solve the right side: $3 + 4 = 7$
3. Compare them: $7 = 7$

Because both sides give you $7$, this equation is true!