Grade 7 Mathematics
An EQUATION is like a balanced scale - both sides must be equal. To solve for a variable, we use INVERSE OPERATIONS to "undo" and isolate the variable.
For TWO-STEP EQUATIONS, work BACKWARDS from order of operations:
1. Undo addition/subtraction FIRST 2. Then undo multiplication/division
Whatever you do to one side of the equation, you MUST do to the other side!
Solve: 3x + 7 = 22
Check: 3(5) + 7 = 15 + 7 = 22 ✓
Identify what's happening to x: It's being multiplied by 3, then 7 is added.
Undo in REVERSE order: First subtract 7 (undo addition), then divide by 3 (undo multiplication).
Always CHECK your answer by substituting back into the original equation!
Like terms have the SAME variable raised to the SAME power. Only like terms can be combined!
Simplify: 5x + 3 - 2x + 8
5x + 3 - 2x + 8
(Group like terms: variables together, constants together)
= (5x - 2x) + (3 + 8)
= 3x + 11
LIKE terms (CAN combine):
3x and 5x → 8x
-2y and 7y → 5y
4 and -9 → -5
UNLIKE terms (CANNOT combine):
3x and 5 → stays 3x + 5
2x and 2y → stays 2x + 2y
x and x² → stays x + x²
The distributive property: a(b + c) = ab + ac — multiply the outside by EVERY term inside!
Expand: 4(x + 3)
4(x + 3)
= 4 · x + 4 · 3
= 4x + 12
Solve: 2(x + 5) = 18
Check: 2(4 + 5) = 2(9) = 18 ✓
WRONG: 3(x + 4) = 3x + 4 (forgot to distribute to the 4!)
RIGHT: 3(x + 4) = 3x + 12 (multiply 3 by BOTH x AND 4)
WRONG: 5x + 3 = 8x (combined unlike terms!)
RIGHT: 5x + 3 = 5x + 3 (cannot combine - different terms)
1. Solve for x: 2x + 9 = 25
x =
2. Solve for y: 5y - 8 = 32
y =
3. Combine like terms: 7a + 4 - 3a + 9
Answer:
4. Expand using distributive property: 6(n + 2)
Answer:
5. Solve: 3(x - 4) = 15
x =