Solving Simple Equations: A Visual Guide

Welcome to understanding balanced equations with Spark.E!Mathematical equations work just like a balanced scale. Both sides must always be equal.When we have equal numbers on both sides, like four equals four, the scale stays perfectly balanced.Now, let's look at an equation like x plus three equals eight.On the left side, we have x plus three, and on the right side, we have eight. The scale stays balanced because these sides are equal.If we add the same number to both sides, like adding two, the equation stays balanced.Similarly, when we subtract the same number from both sides, like subtracting five, the equation remains balanced.Remember the key principle: whatever operation we perform on one side of the equation, we must perform the same operation on the other side to maintain balance.Now that we understand how equations stay balanced, let's learn how to solve for x in the next section.Now that we understand equation balance, let's focus on isolating our variable x.In this equation, we have x plus three equals eight. Our goal is to get x by itself on the left side.To isolate x, we need to move the positive three to the other side. When we move a number, its operation changes to the opposite.Since we're moving a positive three that's being added, it becomes negative three when we subtract it from both sides.We must perform the same operation on both sides to maintain the balance of our equation.Let's review the rules for moving terms from one side to the other.When we move terms across the equals sign, addition becomes subtraction, and subtraction becomes addition.Similarly, multiplication becomes division, and division becomes multiplication.Let's look at another example to reinforce this concept.First, we subtract four from both sides to isolate the term with our variable.This gives us two x equals eight.To get x by itself, we divide both sides by two.And we find that x equals four.Now that we have our solution, let's learn how to verify if it's correct.To verify our solution, we'll substitute x equals 5 back into the original equation.Let's start with our original equation, x plus 3 equals 8.Replace x with 5, giving us 5 plus 3 equals 8.Simplify to get 8 equals 8. Since both sides are equal, our solution is correct!Here's a systematic process for verifying any solution.Let's review some common mistakes to avoid when checking your solutions.The entire process of solving equations can be broken down into three key steps: balance, isolate, and verify.Let's wrap up with some key points to remember about solution verification.Thanks for learning about equation solving and verification with Spark.E!