Solving Linear Equations: Variables on Both Sides

When solving equations, we often encounter situations where variables appear on both sides.An equation is like a balance scale. Both sides must have equal value.On the left side, we have two x plus three. On the right side, we have x plus eight.Let's look at more examples of equations with variables on both sides.Remember these key points about equation structure.When solving equations with variables on both sides, we need to collect all variables together.Here we have two x terms: 2x on the left and x on the right.We need to choose which side to move our variables to.In this case, we'll move terms to the left side since the coefficient of 2x is larger than x.Using the subtraction property of equality, we subtract x from both sides.When we subtract x from 2x on the left, we get x. When we subtract x from x on the right, we get zero.This is an application of the addition and subtraction property of equality - whatever operation we perform on one side must be done to the other side.Now our equation is simpler, with all variable terms on the left side.Now that we have our simplified equation x plus 3 equals 8, let's solve for x.To isolate x, we need to subtract 3 from both sides of the equation.When we subtract 3 from both sides, we get x equals 5.It's crucial to verify our solution by plugging it back into the original equation.Let's start with our original equation: two x plus 3 equals x plus 8.We substitute x equals 5 into both sides of the equation.On the left side, two times 5 plus 3 gives us 13.On the right side, 5 plus 8 also equals 13, confirming our solution is correct.Let's review some common mistakes to avoid when solving equations.First, always remember to perform the same operation on both sides of the equation.Be careful with negative signs when subtracting terms.Never skip the step of checking your solution.And make sure to check your answer in the original equation, not the simplified version.