Subtraction word problems - up to 18

Learning Objectives Translate subtraction-based word problems (with numbers up to 18) into single-variable linear equations. Define a variable to represent an unknown quantity in a given scenario. Formulate an algebraic expression representing a 'take away', 'difference', or 'less than' situation. Solve one-step linear equations involving subtraction using the properties of equality. Interpret the solution of an equation in the context of the original word problem. Verify the solution by substituting it back into the original equation. Distinguish between the initial amount (minuend), the change (subtrahend), and the result (difference) in an algebraic model. You have 15 songs on a playlist and skip some. Now you have 8 left. How can we use al...

TermDefinitionExample VariableA symbol, usually a letter (like x, y, or n), used to represent an unknown quantity or a quantity that can change.In the problem '16 students were on the bus, and some got off. Now there are 7.' We can use the variable 's' to represent the unknown number of students who got off. Algebraic ExpressionA mathematical phrase that contains at least one variable, along with numbers and operation symbols. It does not have an equals sign.If you start with 18 dollars and spend an unknown amount 'd', the expression for the money you have left is '18 - d'. EquationA mathematical statement that asserts the equality of two expressions. It is identified by the presence of an equals sign (=).If you start with 18 dollars, spend 'd&...

Subtraction Property of Equality If \(a = b\), then \(a - c = b - c\) This rule allows you to subtract the same number from both sides of an equation without changing the equation's solution. It is used to undo addition when isolating a variable. Addition Property of Equality If \(a = b\), then \(a + c = b + c\) This rule allows you to add the same number to both sides of an equation. It is useful for eliminating a negative term or moving a subtracted term to the other side. Multiplicative Property of Equality (for negative signs) If \(a = b\), then \(ac = bc\) for \(c \neq 0\) This is used to solve for a variable that has a negative coefficient. For example, if you have \(-x = -5\), you can multiply both sides by -1 to find that \(x = 5\).