Linear Equations
Solve equations of the form ax + b = c
Solving Linear Equations
A linear equation is an equation where the variable has a power of 1. The general form is ax + b = c, where a, b, and c are constants.
Basic Principles
- Equality Property: Both sides of an equation are equal
- Balance Method: Whatever operation you do to one side, do to the other
- Goal: Isolate the variable on one side
Steps to Solve
Step 1: Clear fractions or decimals if present
Step 2: Simplify both sides
Step 3: Get variable terms on one side
Step 4: Get constants on the other side
Step 5: Divide by the coefficient of the variable
Example Problems
Example 1: Solve 2x + 3 = 11
2x + 3 = 11
2x = 11 − 3 (subtract 3 from both sides)
2x = 8
x = 4 (divide both sides by 2)
Example 2: Solve 3x − 5 = 2x + 7
3x − 2x = 7 + 5 (collect variable terms on left, constants on right)
x = 12
Checking Your Solution
Always verify by substituting back into the original equation.
For x = 4 in 2x + 3 = 11: 2(4) + 3 = 8 + 3 = 11 ✓