What is an equation?

An equation is a balance

An equation says that two expressions are equal. Picture a balance scale: whatever sits on the left weighs exactly the same as whatever sits on the right.

The letter $x$ is a variable, a number we don't know yet. Solving the equation means finding the value of $x$ that keeps the scale balanced.

Find the balance point

Here's the same scale, but now you choose $x$. Slide it and watch which way the scale tips. Can you find the value that levels it?

When $x$ is too small, the left pan is too light. When it's too big, the left pan is too heavy. Only one value sits exactly in between.

Checking a solution

A solution is a value that makes the equation true, the value that levels the scale. You don't need a scale to check one: substitute it for the variable and see whether both sides match.

Is $x = 4$ a solution of $x + 3 = 7$?

Both sides match, so yes. What about $x = 5$?

Since $8 \neq 7$, the value $x = 5$ is not a solution.

Variables can be on both sides

The unknown can show up on both pans. Changing $x$ now changes both sides at once, but the right side changes faster. Find the balance point.

Key ideas

• An equation states that two expressions are equal, like a balanced scale.
• A variable stands for a number we don't know yet.
• A solution is the value that balances the scale. Check one by substituting it and seeing whether both sides match.