Grade 6 Mathematics
A variable is a letter that represents an unknown number. We use variables to write expressions (like 3x + 5) and equations (like 2x = 10).
To solve an equation, use inverse operations to get the variable alone!
Translate words into math symbols!
| Words | Algebraic Expression |
|---|---|
| 5 more than a number | x + 5 |
| 3 times a number | 3x (3 times x) |
| A number divided by 4 | x / 4 or x/4 |
| 7 less than a number | x - 7 |
| Twice a number plus 6 | 2x + 6 |
Remember: When a number is right next to a variable (like 3x), it means MULTIPLY! 3x = 3 times x
To evaluate, substitute the given value and calculate!
Example: Evaluate 3x + 7 when x = 4
Step 1: Replace x with 4: 3(4) + 7
Step 2: Multiply: 12 + 7
Step 3: Add: 19
An equation is like a balance. Whatever you do to one side, you MUST do to the other side to keep it balanced!
Use inverse operations to get the variable alone:
Addition <--> Subtraction | Multiplication <--> Division
Example 1: Addition Equation
x + 5 = 12
Subtract 5 from both sides: x + 5 - 5 = 12 - 5
x = 7
Check: 7 + 5 = 12? Yes!
Example 2: Multiplication Equation
4x = 20
Divide both sides by 4: 4x / 4 = 20 / 4
x = 5
Check: 4(5) = 20? Yes!
Example 3: Subtraction Equation
x - 8 = 3
Add 8 to both sides: x - 8 + 8 = 3 + 8
x = 11
Check: 11 - 8 = 3? Yes!
WRONG: x + 5 = 12, so x = 12 + 5 = 17 (Adding to wrong side!)
RIGHT: x + 5 = 12. Subtract 5 from BOTH sides. x = 12 - 5 = 7
1. Write an expression: "8 more than a number" =
2. Write an expression: "A number divided by 5" =
3. Evaluate 2x + 9 when x = 6:
4. Solve: x + 7 = 15, x =
5. Solve: 5x = 35, x =
6. Solve: x - 4 = 9, x =