Model equations using a balance

A balance model represents an equation as two equivalent quantities, with each side composed of known numbers, an unknown, and operations such as addition, subtraction, multiplication, or division; the level position of the balance conveys that both expressions have the same value. This representation supports interpreting the equal sign relationally and connecting changes made to both sides with preservation of equality for linear equations in one variable, without extending to systems, quadratic equations, or other advanced forms.

Detailed Explanation: Model equations using a balance

An equation is like a balanced scale: the expressions on both sides have the same value. The equal sign, $=$ , means “has the same value as,” not just “the answer comes next.”

For example, solve:

3x+2=14

Here:

The left side has three equal groups of $x$ and $2$ extra.
The right side has $14$ .
The balance is level because both sides are equal.

Step 1: Remove the extra $2$

To isolate the groups containing $x$ , subtract $2$ from both sides. Doing the same thing to both sides keeps the balance level:

3x+2-2=14-2

This simplifies to:

3x=12

Step 2: Separate the three equal groups

The $3x$ means three equal groups of $x$ . Divide both sides by $3$ :

\frac{3x}{3}=\frac{12}{3}

So:

x=4

Step 3: Check the balance

Replace $x$ with $4$ in the original equation:

3(4)+2=14

12+2=14

14=14

Both sides have the same value, so the balance is level and the solution is $\boxed{x=4}$ .

Learn by doing: Model equations using a balance

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Balance Shapes - Simple Ratio - To Equations

Earned ?