Equations: keep both sides balanced

Where we are on the map

Equality between expressions becomes a task of finding an unknown value.

Begin with a familiar image

A balance remains level when the same change is made to both pans. The two sides of an equation require the same operation.

Precise meaning

An equation states that two expressions are equal. A solution is a variable value that makes the statement true.

The lesson’s support signal

meaning → model → calculation → check → explain in your own words

same operation on both sides → isolate x → substitute into original → true?

Worked example

3x+5=26; subtract 5 from both sides: 3x=21; divide both sides by 3: x=7; check gives 26=26.

Example with a fading prompt

Change the numbers in the example and repeat the solution without copying its steps. Estimate first, calculate exactly, and check against the original condition.

Recall without a prompt

1. Define the main idea in one sentence.
2. Rebuild the support signal from memory.
3. Solve the example with different numbers and explain why every step is valid.

Find and correct the mistake

Subtracting 5 only on the left and leaving 3x=26 breaks equality. The same change must happen on both sides.

Transfer to a new setting

Apply the same relationship to something you can measure yourself. Name the quantities, units, and the boundary within which the model is valid. Check the answer by a second representation or an inverse operation.

Exercise

Required. Solve 5x−8=27 and 4(x+2)=32; substitute every answer into its original equation.

With your own data. Create one everyday example with the same structure and show it in words, a formula, and a check.

Optional. Seven days later, change the numbers and repeat without the support map.

Open perspective

When two equations must hold together, their common solution forms a system.

Course contents