Lesson: Solving Linear Equations

Objective

Learn how to solve linear equations using various methods.

What is a Linear Equation?

A linear equation is an equation that makes a straight line when graphed. The general form is:

$ax + b = c$

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

Steps to Solve Linear Equations

1. Isolate the variable on one side of the equation.
2. Perform inverse operations to eliminate constants and coefficients.

Example

Solve the equation:

$2x + 3 = 11$

Step 1: Subtract 3 from both sides:

$2x + 3 - 3 = 11 - 3$

which simplifies to:

$2x = 8$

Step 2: Divide both sides by 2:

$\frac{2x}{2} = \frac{8}{2}$

which simplifies to:

$x = 4$

Key Questions

• What is the first step in solving a linear equation?
• How do you check if your solution is correct?
• What changes when the equation has negative coefficients?

Conclusion

Solving linear equations involves isolating the variable through inverse operations. Practice with different examples to strengthen your understanding.