An equation is basically saying that two things are EQUAL since in a balanced situation the two sides of the balance hold equal weight, we can model simple equations with a balance.

In the picture below, each circle represents, “one” (**1**), and the block represents the unknown “**x**“. To find out what the block weighs, you can do the following:

**1. **Add the same amount (circles or blocks) to BOTH sides.**2.** Take away the same amount from BOTH sides. **3.** Multiply BOTH sides by the same amount.**4.** Divide BOTH sides by the same amount.

That way both sides will maintain the balance or “equality”

### Example 1:

The diagram shows a balanced lever. The objects on both sides of the fulcrum (triangle) are equal.

Represent the unknown with the letter **x**

A **block** \( \scriptsize \boxed {?} \) Represents *x* which is unknown

A **circle **\( \Large\circ \) Represents 1

∴ \( \scriptsize x \: + \: 3 = 5 \)

The lever will remain balanced if we removed 3 circles from each side.

We took away three circles from BOTH sides to make the lever balanced.

This reads as one block = two circles.

i.e. x = 2

If x = 2 this can also mean that a block is equal to two circles, which means they both have the same weight.

Therefore the diagram can also be drawn like this;

Without the scale model, the solving process looks like this:

⇒ \( \scriptsize x \: + \: 3 = 5 \)

⇒ \( \scriptsize x \: + \: 3 \: – \: 3 = 5 \: – \: 3 \)

⇒ \( \scriptsize x = 2 \)

### Example 2

⇒ \( \scriptsize 3x \: + \: 2 = 2x \: + \: 6 \)

First, take away two blocks (Two x’s) from both sides.

Then we have \( \scriptsize x \: + \: 2 = 6 \)

Take away two circles from both sides

The balance will stay balanced.

i.e. x = 4

Without the scale model, the solving process looks like this:

\( \scriptsize 3x \: + \: 2 = 2x \: + \: 6 \)**(Take away 2x from both sides)**

**Collect like terms**

**Take away 2 from both sides**

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