Algebra Basics 14Dd83

1. **Stating the problem:** Algebra is a branch of mathematics that uses symbols, usually letters, to represent numbers and express mathematical relationships. 2. **What is algebra?** Algebra helps us solve problems by finding unknown values called variables, often represented by letters like $x$, $y$, or $z$. 3. **Basic formula:** A common algebraic equation looks like this: $$ax + b = c$$ where $a$, $b$, and $c$ are known numbers, and $x$ is the unknown variable we want to find. 4. **Rules to solve algebraic equations:** - You can add, subtract, multiply, or divide both sides of the equation by the same number without changing the equality. - The goal is to isolate the variable on one side of the equation. 5. **Example:** Solve for $x$ in the equation $$3x + 5 = 11$$ 6. **Step 1:** Subtract $5$ from both sides to get rid of the constant term on the left: $$3x + 5 - 5 = 11 - 5$$ which simplifies to $$3x = 6$$ 7. **Step 2:** Divide both sides by $3$ to isolate $x$: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{6}{3}$$ which simplifies to $$x = 2$$ 8. **Answer:** The value of $x$ is $2$. 9. **Summary:** To solve algebra problems, use inverse operations to isolate the variable step-by-step, keeping the equation balanced by doing the same operation on both sides.