Solving Pre-Algebra Equations Step by Step

Welcome to understanding equations! Today, we'll explore how equations work using a balance scale.An equation is like a balance scale, where both sides must always be equal.Let's look at a simple equation: x plus five equals twelve. The x represents an unknown value we want to find.On our balance scale, we can represent this equation with weights. The left side has x plus five, and the right side has twelve.The fundamental rule of equations is that whatever we do to one side, we must do to the other side to maintain balance.To solve for x, we need to isolate it on one side. If we subtract five from both sides, the equation stays balanced.When we remove five from both sides, we can see that x must equal seven to maintain balance.We can verify our answer by plugging seven back into the original equation. Seven plus five equals twelve, confirming our solution.When solving equations, we work with PEMDAS in reverse order.We start with Addition and Subtraction, then Multiplication and Division, followed by Exponents, and finally Parentheses.Let's solve this equation: two x plus six equals twenty.First, we subtract six from both sides to isolate terms with x.This simplifies to two x equals fourteen.Next, we divide both sides by two to isolate x.This gives us our solution: x equals seven.Always verify your solution by plugging it back into the original equation.Let's substitute seven for x in the original equation.Two times seven is fourteen, plus six.Fourteen plus six equals twenty, confirming our solution is correct.Now that we understand the basic process, let's move on to more complex equations.Now let's solve a more complex equation that requires multiple steps.First, we need to distribute the 3 to both terms inside the parentheses.Next, we subtract 6 from both sides to isolate the term with x.Finally, we divide both sides by 3 to solve for x.Before we continue, let's review some common mistakes to avoid.Now let's tackle an equation with variables on both sides.First, we move all terms with x to the left side of the equation.Then we combine like terms, simplifying the left side to x plus 3.Finally, we subtract 3 from both sides to solve for x.After solving any equation, it's crucial to verify your answer.Let's review the key points for solving multi-step equations.Remember, practice and careful attention to detail will help you master these equations.