Solving Equations with Variables on Both Sides

Let's write an equation for this balance scale. The left side has four squares each with weight s. So its total weight is 4s.

The right side has three s squares and a weight of 4. So its weight is 3 s + 4.

Because the scale is balanced, the two sides are equal. This gives us the equation 4 s = 3 s + 4. Now let's solve for s. We can subtract 3s from both sides to keep the scale balanced. On the left, 4 S - 3 S is S. On the right, 3 S - 3 S is zero, leaving 4. So, S= 4. To solve an equation, we perform the same operation on both sides to isolate the unknown.

Let's look at a different problem. On the left, we have six triangles or 6 T plus a weight of three. On the right, there are two triangles 2T at a weight of 11. Since the scale is balanced, we set the sides equal. The equation is 6t + 3 = 2t + 11. To solve this, we first get all the t terms on one side. Let's subtract 2 t from both sides. On the left, 6 t - 2 t is 4 t. On the right, the 2t terms cancel out. Our new equation is 4 t + 3 = 11. Next, let's isolate the 4t term. We can do this by subtracting 3 from both sides to maintain the balance. This leaves us with 4 t on the left and 11 - 3, which is 8 on the right. Now 4 t = 8. To find the value of a single t, we need to undo the multiplication by 4. We'll divide both sides by 4. On the left, 4t t / 4 is t. On the right, 8 / 4 is 2. We've found our answer. t equals 2. By making the same change to both sides of the equation in every step, we were able to find the value of the unknown.