Let's explore the fundamental topic of Algebra: Solving Linear Equations. Algebra is a branch of mathematics dealing with symbols and rules for manipulating those symbols, where letters (called variables) are used to represent numbers.

Topic: Solving Linear Equations

A linear equation is an equation of the form: $ax + b = 0$ where:

• $x$ is the variable,
• $a$ and $b$ are constants.

The goal is to solve for $x$, which means finding the value of $x$ that makes the equation true.

Example Problem:

Solve the equation: $2x + 3 = 7$

Steps to Solve:

1. Isolate the variable term by subtracting 3 from both sides: $2x + 3 - 3 = 7 - 3$ Simplifying: $2x = 4$

2. Solve for $x$ by dividing both sides by 2: $\frac{2x}{2} = \frac{4}{2}$ Simplifying: $x = 2$

The solution is $x = 2$.

Verification:

Substitute $x = 2$ back into the original equation: $2(2) + 3 = 7$ $4 + 3 = 7$ Since both sides are equal, the solution is correct.

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Key Points:

1. Linear equations have the form $ax + b = 0$.
2. The goal is to isolate the variable $x$ on one side of the equation.
3. To isolate $x$, use basic operations: addition, subtraction, multiplication, and division.

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Would you like more details or have any questions about solving linear equations?

Here are five related questions:

1. What happens when $a = 0$ in the equation $ax + b = 0$?
2. How do you solve an equation with variables on both sides, like $3x + 2 = 5x - 4$?
3. How can you solve equations with fractions, such as $\frac{2x}{3} + 1 = 5$?
4. What does it mean if the equation has no solution?
5. How do you graph a linear equation on a coordinate plane?

Tip: When solving equations, always check your solution by substituting it back into the original equation.