An algebraic equation is like a sentence, except with an equal sign in place of the word is. When you see 7 − x = 14, for example, that's just the math way of saying "seven minus some number is fourteen." The unknown number, represented here by an x (although any letter will do) is called a variable. "Solving" an equation means isolating the variable on one side of the equal sign, as in x = 4 or y = -5. When an equation looks like this, it cannot be simplified any further.
To isolate the variable, and thereby solve the equation, we use inverse operations. In math, inverse just means opposite. Addition and subtraction are inverse operations, as are multiplication and division. So, if the variable is being multiplied by a number, we divide both sides by that number. If the variable is being added to another number, we subtract that number from both sides. Always, the goal is to get that variable alone on one side of the equal sign.
Here's an example: 4x = 24. This equation could be expressed in words as "four times a number is 24." To solve, we isolate the variable by performing the inverse function. Since the x is being multiplied by 4 in the original version of the equation, we divide each side by 4 to obtain the answer: 4x ÷ 4 = 24 ÷ 4. This leaves us with x = 6. The equation has been solved!
In this introductory lesson, we're just looking at simple, one-step equations. Here are a few for you to try!