What are inverse operations?
Operations that undo each other (e.g., addition and subtraction).
Define 'like terms'.
Terms with the same variable raised to the same power.
State the distributive property.
$a(b + c) = ab + ac$
What does 'isolating a variable' mean?
Getting the variable alone on one side of the equation.
What is SADMEP?
The reverse order of operations: Subtraction, Addition, Division, Multiplication, Exponents, Parentheses.
What are coefficients?
The numbers in front of the variables.
How do you isolate a variable using inverse operations?
Perform the opposite operation on both sides of the equation.
How do you combine like terms?
Add or subtract their coefficients.
How do you apply the distributive property?
Multiply the term outside the parentheses by each term inside.
What's the first step when solving equations with variables on both sides?
Gather all variable terms to one side of the equation.
Solve for $x$: $x + 8 = 15$
Subtract 8 from both sides: $x = 7$
Solve for $y$: $5y = 35$
Divide both sides by 5: $y = 7$
Simplify: $3x + 5x - 2 = 14$
Combine like terms: $8x - 2 = 14$. Add 2 to both sides: $8x = 16$. Divide by 8: $x = 2$
Solve: $2(x + 4) = 18$
Distribute: $2x + 8 = 18$. Subtract 8: $2x = 10$. Divide by 2: $x = 5$
Solve: $4x - 2 = 2x + 6$
Subtract $2x$: $2x - 2 = 6$. Add 2: $2x = 8$. Divide by 2: $x = 4$
