Solving One-Step and Two-Step Equations

Let's learn how to solve equations using a balance scale. In this first problem, the left side has a square of unknown weight s plus a weight of four. The right side has a weight of 11. Since the scale is balanced, we can write the equation s + 4 = 11.

To find the weight of s, we need to get it by itself. This is called isolating the variable. To do this, we can remove the four from the left side. To keep the scale balanced, we must also remove four from the right side. Subtracting four from each side keeps the equation balanced. Let's try another one. On the left, we have six identical triangles, each with a weight of t. This means the total weight on the left is 6 * t or 6t.

The right side has a weight of 12. The equation is 6t = 12. Our goal is to find the weight of a single triangle t.

Since the left side is 6 * t, we can use the inverse operation, which is division, to isolate t. When we divide the left side by six, we're left with one t. To maintain the balance, we also divide the right side by six. This shows that one triangle t has a weight of two.

Let's solve a two-step equation. First, we can write the equation for this scale. On the left, we have four circles, each with weight C plus a weight of three. On the right, we have a weight of 11. So, the equation is 4 C + 3 = 11.

To solve this equation, we first need to get the 4 C term by itself. Subtracting three from both sides leaves us with a simpler balanced equation. 4 C= 8.

Next, we can divide both sides by four.

This gives us our final answer. c= 2. We just solved equations by making balanced changes to each side.