MATH
1. What is Algebra?
Imagine you have a treasure chest, but you don't know what's inside it.
You can call the mystery item a letter, like x. Algebra is all about finding out what x is!
Example:
If x + 3 = 7, what's in the chest?
To figure it out, think:
● What plus 3 equals 7?
● The answer is 4, SO x = 4.
You've solved the puzzle!
2. Combining Like Things
Let's say you're collecting apples and oranges:
● You have 3 apples and then get 2
more apples. That's 3 + 2 = 5
apples!
● But if you mix apples and oranges, you can't combine them:
3 apples + 2 oranges stays as
За + 20.
In Algebra Terms:
Combine only the same "types" of letters, like x + x :
= 2x, but x+ y
stays x + y.
3. Equations: Balancing a
Scale
Think of an equation as a scale that needs to stay balanced.
● Example: If one side has x + 3 and the other side has 7: x+3=7.
● To balance it, take 3 away from both sides:
x+3-3=7-3,50 x=4.
, Why? Whatever you do to one side, you must do to the other to keep things fair!
4. Solving Bigger Problems
What if the treasure chest is
heavier, like 2x + 3 = 9?
• First, get rid of the extra 3 by subtracting it:
2x+3-3=9-3,502x=6.
• Then, split the 2x into 2 equal parts:
x = 6 ÷ 2,50 x=3.
5. Fun Tip: Use Stories!
Imagine x as a superhero who's always trying to save the day by figuring out the answer.
Every time you solve for x, you're helping the superhero finish their mission!
1. Systems of Linear Equations
Definition: A system of equations is a set of two or more equations with the same variables.
The goal is to find the values of the variables that satisfy all equations.
Methods of Solving:
● Substitution
● Elimination
● Graphing
Example (Substitution):
Solve the system:
2x + y=10 and x-y=2
1. What is Algebra?
Imagine you have a treasure chest, but you don't know what's inside it.
You can call the mystery item a letter, like x. Algebra is all about finding out what x is!
Example:
If x + 3 = 7, what's in the chest?
To figure it out, think:
● What plus 3 equals 7?
● The answer is 4, SO x = 4.
You've solved the puzzle!
2. Combining Like Things
Let's say you're collecting apples and oranges:
● You have 3 apples and then get 2
more apples. That's 3 + 2 = 5
apples!
● But if you mix apples and oranges, you can't combine them:
3 apples + 2 oranges stays as
За + 20.
In Algebra Terms:
Combine only the same "types" of letters, like x + x :
= 2x, but x+ y
stays x + y.
3. Equations: Balancing a
Scale
Think of an equation as a scale that needs to stay balanced.
● Example: If one side has x + 3 and the other side has 7: x+3=7.
● To balance it, take 3 away from both sides:
x+3-3=7-3,50 x=4.
, Why? Whatever you do to one side, you must do to the other to keep things fair!
4. Solving Bigger Problems
What if the treasure chest is
heavier, like 2x + 3 = 9?
• First, get rid of the extra 3 by subtracting it:
2x+3-3=9-3,502x=6.
• Then, split the 2x into 2 equal parts:
x = 6 ÷ 2,50 x=3.
5. Fun Tip: Use Stories!
Imagine x as a superhero who's always trying to save the day by figuring out the answer.
Every time you solve for x, you're helping the superhero finish their mission!
1. Systems of Linear Equations
Definition: A system of equations is a set of two or more equations with the same variables.
The goal is to find the values of the variables that satisfy all equations.
Methods of Solving:
● Substitution
● Elimination
● Graphing
Example (Substitution):
Solve the system:
2x + y=10 and x-y=2
