What is Algebra?
Algebra is like solving a puzzle where you need to solve for the missing pieces. It’s all about using numbers, symbols, and operations to find answers to problems—even when you don’t have all the information. If you’ve ever wondered how to figure out the total cost of something on sale, split a bill evenly with friends, or predict how much time you’ll need to finish a homework assignment, you’ve already used algebra without realizing it!
What is the Definition of Algebra
Algebra is a branch of math that uses symbols (like letters) to represent numbers. These symbols, called variables, stand in for values that might change or aren’t known yet. Instead of solving math problems with just numbers, algebra teaches you how to work with these variables to find answers.
Key Parts of Algebra
Variables: Letters like x or y that represent unknown numbers. For example, in 2x + 5 = 15, x is the variable you need to figure out.
Expressions: Expressions are mathematical phrases made up of some combination of numbers, variables, and operations (like addition or multiplication), such as 4x + 2.
Equations: They are like math sentences where two things are equal, such as 3x = 12. Solving equations means finding the value of the variable.
Functions: Rules that show the relationship between two sets of numbers. For example, a function could show you how many miles you can drive based on how much gas you have.
What is the equals sign?
The equals sign indicates balance, which must be maintained no matter what manipulation is performed on the equation. You may square an equation, subtract 10,000, add 0.00001, and perform almost any other mathematical operation you can think of—so long as it’s done to both sides of the equals sign. Just please do not divide by zero! This is not allowed as the result is undefined.
In simpler terms, what’s done on one side must be done to the other. You can think of this concept like a set of scales, where the scale acts as the equals sign.
When the equation starts out, the two sides are equal. In the picture above, we see that two squares equal six circles.
If we want to see how much one square weighs, we remove one square from the left side without removing anything on the right.
The scale above shows what happens when we remove one square from the left. The scale, or the equals sign, is no longer balanced. This breaks the rules of mathematics.
To balance this particular scale, we must remove three circles from the right side.
This scale is once again balanced, and we can clearly see that one square equals three circles.
So, what did we just show? Maintaining an equation’s balance is a crucial component of Algebra, a branch of mathematics that uses letters and symbols to describe relationships between known and unknown values. Algebra can become more complex the deeper you dive into the subject, but if you follow the mathematical ruleset you’ll be able to find the answer to the equation at hand.
What Will You Learn in Algebra?
Algebra covers a wide range of topics, but each topic builds upon each other. Here are some main topics you’ll likely study?
Linear Equations:
These are equations like y = 2x + 3 that describe straight lines when you graph them. You’ll learn how to solve these equations and see how changing one number affects the whole equation.
Inequalities:
Sometimes, instead of finding an exact answer, you need to figure out a range of possibilities. Inequalities, like x > 3, teach you how to do this.
Quadratic Equations:
These equations involve variables squared (like x2). They might look complicated at first, but you’ll learn tools like factoring and the quadratic formula to make them manageable.
Exponents and Polynomials
Exponents and Polynomials introduce powers (like x3) and multi-term expressions, helping you tackle bigger and more complex problems.
How to Make Algebra Easier
If algebra feels tough right now, that’s okay! Everyone starts somewhere, and the more you practice, the easier it gets. Here are some tips to help:
Start with the Basics: Make sure you’re comfortable with foundational arithmetic like addition, subtraction, and fractions. These are the building blocks for algebra.
Break Problems Into Steps: Don’t try to solve everything at once. Tackle one part of the problem at a time. Check out our article on simplifying and interpreting Algebra to break down problems into steps.
Ask Questions: If something doesn’t make sense, speak up! Teachers or classmates can explain it in a way that clicks for you.
Use Tools Like UPchieve: A free UPchieve algebra tutor can guide you through tricky topics and help you feel more confident.
How UPchieve Can Help
Algebra doesn’t have to be something you struggle with alone. UPchieve offers free, on-demand tutoring to help you tackle your questions, whether you’re stuck on homework, preparing for a test, or just trying to figure out a tough concept.
Why Choose UPchieve for Algebra?
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Get Started with an Algebra Tutor Today
Algebra isn’t just a subject—it’s a skill that helps you think critically, solve problems, and understand the world in new ways. Whether you’re learning the basics or tackling complex equations, building a strong foundation in algebra can open doors to exciting opportunities.
Ready to get started? Sign up for UPchieve and connect with a free tutor who can help you make sense of algebra, one problem at a time.
Algebra FAQs
What can my Algebra tutor help with?
UPchieve’s Algebra tutors can help with everything from basic equations to advanced topics like functions and quadratic equations. If you’re working on a specific concept, just ask—we’re here to help.
Is algebra tutoring really free?
Yes! Thanks to our generous supporters, UPchieve provides free algebra tutoring for middle and high school students across the U.S.
Can I get help with my algebra homework?
Absolutely! Our tutors can guide you through assignments, explain confusing steps, and help you feel confident about solving problems on your own.
What if I’m preparing for an algebra test?
No problem! Whether it’s a quiz, a midterm, or even an AP exam, our tutors can help you review concepts, practice problems, and get ready to succeed. Preparing for the ACTs? We can help you prepare for the ACT Math Section, too!
How do I get matched with a tutor?
Sign up for a free account on UPchieve, choose “Math,” and select “Algebra.” You’ll be matched with a tutor in just a few minutes.
Additional Resources for Algebra
Looking for more resources to help you with math? Check out these articles for additional math homework help: