01 Key Concepts
What Makes an Equation Linear
Every variable term has an exponent of exactly 1 (no x^2, sqrt(x), or 1/x terms) — its graph is always a straight line.
The Balance Principle
Whatever operation you do to one side of an equation, you must do to the other side too, to keep both sides equal.
Solving Multi-Step Equations
Use inverse operations in reverse order of PEMDAS: undo addition/subtraction first, then multiplication/division, isolating the variable last.
Variables on Both Sides
Move all variable terms to one side and all constants to the other by adding or subtracting the same term from both sides.
Checking Solutions
Substitute your answer back into the original equation; both sides should come out equal.
02 Key Formulas
- If a = b, then a+c = b+c, a-c = b-c, a*c = b*c, and a/c = b/c (c not 0)
03 Solved Examples
Example 1 Solve for x: 3x + 5 = 20.
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 15/3.
Answer: x = 5
Example 2 Solve for x: 2x + 7 = x + 15.
- Subtract x from both sides: x + 7 = 15.
- Subtract 7 from both sides: x = 8.
Answer: x = 8
Example 3 Solve for x: 4(x - 2) = 16.
- Distribute the 4: 4x - 8 = 16.
- Add 8 to both sides: 4x = 24.
- Divide by 4: x = 6.
Answer: x = 6
04 Practice Questions
1Solve for x: 2x + 3 = 11.
x = 4
2Solve for x: 5x - 4 = 16.
x = 4
3Solve for x: 3x + 2 = x + 10.
x = 4
4Solve for x: 2(x + 3) = 14.
x = 4
5Check: is x=5 a solution to 3x - 5 = 10?
Yes, 3(5)-5=10
📄 Linear Equations — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.