Glossary
Distributive property
A property stating that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products (e.g., a(b + c) = ab + ac). It's used to remove parentheses in equations.
Example:
When calculating the total cost for 3 friends each buying a 2 snack, you can use the distributive property: 3(2) = 3(2).
Inverse operations
Mathematical operations that undo each other, such as addition and subtraction, or multiplication and division. They are used to move terms across the equals sign and isolate variables.
Example:
To solve for 'x' in x - 7 = 10, you'd use the inverse operation of addition by adding 7 to both sides.
Isolating a variable
The process of manipulating an equation to get a specific variable by itself on one side of the equals sign, revealing its value.
Example:
To find out how many hours you studied, you might need to isolate the variable 'h' in the equation 2h + 5 = 15.
Like terms
Terms in an algebraic expression that have the same variable(s) raised to the same power. They can be combined by adding or subtracting their coefficients.
Example:
In the expression 5x + 3y - 2x, '5x' and '-2x' are like terms because they both contain the variable 'x' raised to the first power.
SADMEP
An acronym representing the reverse order of operations (Subtraction, Addition, Division, Multiplication, Exponents, Parentheses), used as a strategy to undo operations when isolating a variable.
Example:
When solving a complex equation like 3(x+2) - 5 = 10, remembering SADMEP helps you know to add 5 first, then divide by 3, before dealing with the parentheses.
Variables on both sides
An equation where the unknown variable appears on both the left and right sides of the equals sign. Solving these requires moving all variable terms to one side and constant terms to the other.
Example:
A common SAT problem might ask you to solve an equation like 4x - 8 = 2x + 4, which has variables on both sides.