Review the key concepts, formulae, and examples before starting your quiz.
πConcepts
Definition of a Linear Equation: An equation where the highest power of the variable (usually x) is 1.
The Golden Rule of Algebra: Whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side to keep it balanced.
Inverse Operations: Use subtraction to undo addition, addition to undo subtraction, division to undo multiplication, and multiplication to undo division.
Isolating the Variable: The goal is to get the variable alone on one side of the equals sign.
Expanding Brackets: If an equation contains brackets, use the distributive law before solving.
Variables on Both Sides: Collect all terms containing the variable on one side and all constant numbers on the other side by adding or subtracting terms.
πFormulae
General form:
Distributive Property:
Fractional Equations:
Cross Multiplication: If \frac{a}{b} = rac{c}{d}, then
π‘Examples
Problem 1:
Solve
Solution:
Explanation:
Step 1: Add 7 to both sides to undo the subtraction (). Step 2: Divide both sides by 4 to isolate x ().
Problem 2:
Solve
Solution:
Explanation:
Step 1: Expand the brackets (). Step 2: Subtract 3 from both sides (). Step 3: Divide by 6 ().
Problem 3:
Solve
Solution:
Explanation:
Step 1: Subtract from both sides to get all variables on the left (). Step 2: Add 4 to both sides (). Step 3: Divide by 3 ().
Problem 4:
Solve
Solution:
Explanation:
Step 1: Multiply both sides by 2 to remove the denominator (). Step 2: Subtract 4 from both sides ().