Equation Balance Scale

Type any one-step or two-step linear equation and watch it get solved on a balance scale. Each operation is applied to both sides, showing you exactly how the algebra works. All computation runs in your browser.

Enter an equation

Supports equations like ax + b = c, ax = b, or x + b = c

Try an example

Solution

x = 4

Step-by-Step Solution

1Start with the original equation

2x + 3 = 11

2Subtract 3 from both sides

2x + 3 \; {\color{teal}- 3} = 11 \; {\color{teal}- 3}

3Simplify

2x = 8

4Divide both sides by 2

\frac{2x}{\color{teal}2} = \frac{8}{\color{teal}2}

5Solution

x = 4

Reference Guide

One-Step Equations

A one-step equation needs only one operation to isolate the variable. For example, with $5x = 30$ , divide both sides by 5.

\frac{5x}{5} = \frac{30}{5} \implies x = 6

The key idea is that whatever you do to one side of an equation, you must do the same to the other side.

Two-Step Equations

A two-step equation requires two operations. First undo addition or subtraction, then undo multiplication or division.

2x + 3 = 11

Step 1: Subtract 3 from both sides to get $2x = 8$ .

Step 2: Divide both sides by 2 to get $x = 4$ .

The Balance Model

Think of an equation as a balance scale. The left side and the right side weigh the same. If you add or remove weight from one side, you must do the same to the other to keep the scale balanced.

This is why we always perform the same operation on both sides. The goal is to get the variable alone on one side, which tells us its value.

Checking Your Answer

Always verify your solution by substituting it back into the original equation. If both sides are equal, the solution is correct.

2(4) + 3 = 8 + 3 = 11 \; \checkmark

If the sides are not equal, go back and check each step for arithmetic errors.