Grade 10 Math: Algebra Basics Explained

Welcome to the first step in our algebra journey, where we'll explore variables and expressions.A variable is simply a letter that stands in for a number we don't know yet.For example, x can represent any unknown value. It could be your age in five years, the number of pets you have, or tomorrow's temperature.Now, let's look at how we combine variables with numbers to create expressions.In the expression two x plus five, we have several components.Let's practice translating words into mathematical expressions.Now let's practice identifying components in different expressions.These fundamental concepts will help us as we move forward in our algebra journey.When solving equations, we must always maintain balance - what we do to one side, we must do to the other.Here we have three x equals twelve. To solve for x, we divide both sides by three.When solving equations with like terms, first combine similar variable terms.For equations with parentheses, distribute first before combining terms.Let's solve a real-world budget problem.Finally, let's solve a problem involving time and tasks.Let's solve our first word problem about age relationships.We'll follow these steps to solve any word problem systematically.Let's solve this step by step. First, we let x represent the sister's current age.We can write the equation: twenty-four equals three times what the sister's age was four years ago.Distribute the three.Add twelve to both sides.Divide both sides by three. The sister is twelve years old.Now let's solve a distance-rate-time problem.We'll use the distance equals rate times time formula.Plugging in our values: four hundred and eighty equals rate times four.Solving for rate, we get one hundred and twenty kilometers per hour.Let's solve our final problem about percentage increases.For percentage problems, we first calculate the increase, then add it to the original amount.Fifteen percent of eighty dollars is twelve dollars.Adding twelve to the original price of eighty gives us ninety-two dollars.