Solving Addition and Subtraction Equations

An equation is a mathematical statement that two expressions are equal. Think of the equals sign $=$ as the center of a balance scale. For the scale to stay level, the value on the left must be exactly the same as the value on the right. Our goal is to find the value of the variable (the unknown letter, like $x$) by getting it all by itself on one side of the equation. This is called isolating the variable. To keep the 'scale' balanced, if you add or subtract a number from one side, you must do the exact same thing to the other side.

To solve equations, we use inverse operations, which are operations that 'undo' each other. Addition and subtraction are opposites. If an equation has subtraction, you 'undo' it by adding. For example, in the equation $x - 8 = 10$, the $x$ is having 8 taken away from it. To get $x$ alone, we must add 8 back to both sides. This keeps our mathematical scale perfectly level while revealing the hidden value of our variable.

The best part about algebra is that you can always check if you are right! Once you find a value for your variable, substitute (plug) it back into the original equation. If the left side equals the right side, your answer is 100% correct. This turns every math problem into a puzzle you can solve with total confidence. Even if the equation looks backwards, like $20 = x + 5$, the rules remain exactly the same: keep it balanced!