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Introduction to Algebra

What is x? Solve puzzles by finding where two lines cross

Algebra is like a puzzle: you have a mystery number (called x), and you need to figure out what it is. If someone tells you x + 3 = 7, you're looking for the number that, when you add 3 to it, gives you 7. The answer? x = 4, because 4 + 3 = 7.

But here's the cool part: you can see the answer on a graph. Plot y = x + 3 as a line and y = 7 as another line. Where they cross is your answer — the x-value at that point is the mystery number.

In this lesson, you'll solve algebra puzzles visually, starting simple and building up. No memorizing rules — just find where the lines meet, and you've solved the equation!

Graph

FAQ

What is algebra?
Algebra is a branch of math where you use letters (like x) to stand for unknown numbers, and then figure out what those numbers are. It's like solving a puzzle: "what number plus 3 equals 7?" In algebra, you'd write that as x + 3 = 7 and solve to get x = 4.
What is a variable?
A variable is a letter that represents an unknown number. The most common one is x, but you can use any letter. In x + 3 = 7, the variable x stands for the number 4 — because 4 is the number that makes the equation true.
How do I solve for x?
You can solve for x algebraically (undo operations step by step) or graphically (plot both sides and find where they cross). For x + 3 = 7: algebraically, subtract 3 from both sides to get x = 4. Graphically, plot y = x + 3 and y = 7, and read the x-value where they intersect.
Why do we use graphs to solve equations?
Graphs make equations visible. Instead of manipulating symbols, you can see the answer as the point where two lines cross. This builds intuition — you understand that solving an equation means finding where two expressions have the same value. It also works for harder equations where algebraic tricks are difficult.