The concept of solving linear equations involves finding the value(s) of the variable(s) that make the equation true. A linear equation is an equation where the highest power of the variable is 1, meaning it graphs as a straight line when plotted. The general form of a linear equation in one variable is:

$ax + b = 0$

where:

• $x$ is the variable,
• $a$ and $b$ are constants (real numbers),
• $a \neq 0$.

Steps to Solve Linear Equations:

1. Isolate the variable: Move terms involving the variable to one side of the equation, and constant terms to the other.
2. Simplify the equation: Combine like terms if necessary, simplifying both sides.
3. Solve for the variable: Divide or multiply to solve for the unknown variable.
4. Check the solution: Substitute the value back into the original equation to ensure it satisfies the equation.

Example:

$3x + 5 = 11$

Step 1: Subtract 5 from both sides to isolate the term with $x$:

$3x = 11 - 5$

$3x = 6$

Step 2: Divide both sides by 3 to solve for $x$:

$x = \frac{6}{3} = 2$

Step 3: Verify the solution by substituting $x = 2$ into the original equation:

$3(2) + 5 = 6 + 5 = 11$

Thus, $x = 2$ is the correct solution.

Types of Linear Equations:

1. One variable: $ax + b = 0$ (e.g., $3x - 7 = 2$).
2. Two variables: $ax + by = c$ (e.g., $2x + 3y = 7$).
3. Systems of linear equations: Multiple linear equations that share the same variables, solved simultaneously.

Would you like further details or clarifications?

Related Questions:

1. How do you solve a linear equation with fractions?
2. What are the methods to solve systems of linear equations?
3. How do you graph a linear equation on the coordinate plane?
4. What is the difference between consistent and inconsistent systems of linear equations?
5. How can you apply linear equations in real-world problems?

Tip:

When solving linear equations, always perform the same operation on both sides to maintain the balance of the equation.