Math With AmarA C A D E M Y
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Middle school · Linear equations

Solve while keeping both sides equal

Remove the same constant from both sides, then divide equal groups to reveal x.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Solve while keeping both sides equal. Current stage: Start / removing the constant. Left-hand value: 18. Right-hand value: 183x + 6 = 18Subtract 6 from both sides+6+6xxx12444Equal changes keep the balance level
This visual uses positive integer coefficients and solutions, with a nonnegative added constant. The balance is a symbolic equality model, not a physical simulation. Algebraic readouts update at the completed subtraction and division stages.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Current stage
Start / removing the constant
Left-hand value
18
Right-hand value
18

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

An equation is a statement of equal values. Subtracting the same number from both sides preserves that statement. When several identical x-boxes remain, dividing both sides by the same nonzero number isolates one box. Substitution checks that the result still satisfies the original equation.

A relationship to keep

ax + b = c → ax = c − b → x = (c − b)/a

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Create a balanced equation

    Choose the hidden value, the number of identical boxes, and the added constant. The right-hand total is calculated to make the original equation true.

  2. STEP 2

    Subtract on both sides

    In the first half of the animation, equal constant tiles leave both pans together. At the halfway point, only the identical x-boxes and their combined value remain.

  3. STEP 3

    Divide into equal shares

    In the second half, the known total is separated into the same number of equal shares as there are boxes. At the end, one highlighted share identifies x. Multiply and add back to check the starting equation.

Your turn to explain

Make a prediction. Test your reasoning.

Solve 4x + 7 = 31. Which operation comes first, and what is x?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

Subtract 7 from both sides to get 4x = 24. Then divide both sides by 4, giving x = 6. Check: 4 × 6 + 7 = 31.

Work through a full lesson

Connect the animation to a worked example and practice questions.

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