⚖️ The Equation Balance

This is a balance scale. When both pans hold the same weight, the scale stays level. We do not know how many weights are hidden in the mystery bag on the left pan. Let’s call that number x. The scale is balanced, so x + 2 = 5.

If one pan is heavier, the scale tips. If we add the same weight to the other pan, the balance comes back. Here is the rule: whatever you do to one side, do the same to the other side. That is how both a scale and an equation stay balanced.

Now a bigger scale. The left pan has 2 bags and 3 weights, and the right pan has 11 weights. Both bags hide the same number of weights. Let’s write the equation: 2x + 3 = 11.

Let’s get x on its own. First we take 3 weights off the left pan. To keep the scale balanced, we take 3 weights off the right pan too. That leaves 2 bags and 8 weights: 2x = 8.

Now let’s take half of each pan: 1 bag is left on the left, and 4 weights on the right. Each bag hides 4 weights: x = 4. We undid the multiplying by dividing.

Let’s check the answer. We put 4 weights in place of each bag. The left pan has 2 × 4 + 3 = 11 weights, and the right pan has 11 too. The scale is balanced, so x = 4 is right. This is called checking your answer.

Let’s write an equation from a story. Sam’s age is x. Sam’s brother is 17 years old. His age is 3 more than double Sam’s age. Let’s show it with boxes: two x boxes and one 3 box make 17. The equation: 2x + 3 = 17.

Let’s solve it. If we take 3 from both sides, we get 2x = 14. Then we divide by two: x = 7. Sam is 7 years old! Check: 2 × 7 + 3 = 17, which is the brother’s age.

Summary: an equation is a balance. Whatever you do to one side, do to the other side too. First undo adding and subtracting, then multiplying and dividing. At the end, check your answer. Now try it in Algebra Castle!