Across
- 3. the Variable, The goal of solving an equation. To get the variable by itself on one side of the equals sign, usually through the use of inverse operations.
- 4. The process of replacing a variable with a numerical value to check if it is a solution to an equation. Plugging the solution back in should make the equation true.
- 5. A number that multiplies a variable. In the term 5x, the coefficient is 5.
- 6. Solutions, An equation that is true for all possible values of the variable. When solved, the result is a true statement (e.g., 2 = 2). The two sides of the equation are identical.
- 10. A mathematical phrase that can contain numbers, variables, and operators (like +, -), but no equals sign. Example: 3y - 7
- 12. A symbol (usually a letter) that represents an unknown number or a value that can change. Examples: x, a, n
- 13. A mathematical statement that shows two expressions are equal. It contains an equals sign (=). Example: 2x + 5 = 11
- 16. A single number, a variable, or numbers and variables multiplied together. Terms are separated by + or - signs. Example: The expression 4x² - x + 6 has three terms.
- 17. Operation, Operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. We use these to solve equations.
Down
- 1. Method, The fundamental principle for solving equations: whatever operation is done to one side of the equation must be done to the other side to keep it balanced or equal.
- 2. Property, A property that states a(b + c) = ab + ac. It is used to multiply a term across terms inside parentheses. Example: 3(x + 4) = 3*x + 3*4 = 3x + 12
- 4. To perform all possible operations in an expression or equation to rewrite it in its most basic or compact form. This often involves combining like terms.
- 6. The set of whole numbers and their negatives: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
- 7. Solution, An equation that has no possible answer. When solved, the result is a false statement (e.g., 5 = 0). The equation is never true.
- 8. Equation, An equation that requires more than one operation (e.g., combining like terms, using the distributive property, then using inverse operations) to solve.
- 9. Terms, Terms that have the exact same variables raised to the same exponents. Their coefficients can be different. Example: 3x and -8x are like terms; 2y and 2y² are not.
- 11. A fixed value that does not change. It is a number on its own. In the expression 2x + 9, the constant is 9.
- 14. Number, Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0. This includes integers, fractions, terminating decimals, and repeating decimals.
- 15. Solution, An equation that has exactly one numerical answer for the variable. Example: x = 5.
- 18. on Both Sides, An equation where the unknown variable appears on both sides of the equals sign. The first step is usually to move all variable terms to one side.