Introduction to equations
Equations with positive integer solutions
Background
Know the timetable
Working with fractions
Working with decimals
Dividing by 2 digit numbers
Key words
Equation
: a mathematics sentence with an equal sign
Goal
Be able to solve algebraic equations such as
3n - 4 = 8
5x + 3 = 23
Communicate
Describe steps to solve an equation
Key concepts
Whatever you do on one side of the equation, you do the exact on the other side of the equation
Undo the operation(s) on both sides of the equation to solve the equation
Three ways to remember this:
Apply inverse operations
Apply opposite operations
Undo the operation
Patterns in solving equations
Equation
Integers
Decimals
Fractions
x + a = b
x + 3 = 5
x + 3.2 = 5.1
x + 1/4 = 5/2
x - a = b
x - 3 = 5
x - 3.2 = 5.1
x - 1/4 = 5/2
-x = a
-x = 5
-x = 5.1
-x = 5/2
-x = -a
-x = -5
-x = -5.1
-x = -5/2
ax = b
2x = 8
2.5x = 12.5
(2/3)x = 3/4
ax = -b
2x = -8
2.5x = -12.5
(2/3)x = -3/4
-ax = b
-2x = 8
-2.5x = 12.5
(-2/3)x = 3/4
-ax = -b
-2x = -8
-2.5x = -12.5
(-2/3)x = -3/4
ax + b = c
2x + 3 = 11
2.5x + 3.2 = 12.5
(2/3)x + 3/4 = 1/2
ax + b = cx + d
5x + b = 2x + d
1.5x + 3 = 3.5x + 2.5
(2/3)x + = (7/2)x + 5/2
a(x + b) + c = d(x + e) + f
5(x + 2) + 2 = 3(x+3) + 5
5.1(x + 2) + 2.3 = 3(x+3.4) + 5
(2/3)(x + 2) + 2 = (5/2)(x+3) + 5/3
Ideas
Collect like terms.
After collecting like terms, you should end up with only 2 terms.
Move the term containing the variable to one some of the equation, and the numerical term to the other side of the equal sign
Solve the equation
Try it out
GetEquation
Visualization
The balance beam
Expectations
Be able to solve single variable (linear) equations
Inverse operations: pages 52-55
Unit 2 test
Unit 2 test: page 67