Balance subtraction equations - up to two digits

Learning Objectives Translate word problems involving subtraction into linear equations and inequalities. Apply the Subtraction Property of Equality to isolate variables in multi-step linear equations. Apply the Subtraction Property of Inequality to isolate variables in multi-step linear inequalities. Solve linear equations and inequalities that involve the subtraction of binomial expressions. Represent the solution set of a linear inequality on a number line. Verify solutions to linear equations and inequalities by substitution. Distinguish between the single-value solution of a linear equation and the solution set of a linear inequality. Imagine you have a $95 gift card and want to buy a game, but you also have to pay for a subscription. How do you figure out the maximum...

TermDefinitionExample Linear EquationA mathematical statement asserting that two expressions are equal, forming a straight line when graphed. It has one or more variables, and the highest power of the variable is 1.90 - 5x = 25 Linear InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥). The solution is a range of values, not a single number.75 - (2x + 10) > 30 Isolating the VariableThe process of performing inverse operations to get a variable by itself on one side of the equation or inequality.To isolate x in x + 15 = 40, we subtract 15 from both sides. Inverse OperationsOperations that 'undo' each other. Subtraction is the inverse operation of addition.To undo the subtraction of 20 in the expression y - 20, you woul...

Subtraction Property of Equality If \(a = b\), then \(a - c = b - c\) You can subtract the same number, variable, or expression from both sides of an equation, and the equation will remain balanced. Subtraction Property of Inequality If \(a > b\), then \(a - c > b - c\). This also applies to \(<, \le, \ge\). You can subtract the same number, variable, or expression from both sides of an inequality without changing the direction of the inequality symbol. Distributing a Negative \(-(a + b) = -a - b\) and \(-(a - b) = -a + b\) When subtracting an expression in parentheses, you must distribute the negative sign to every term inside the parentheses, effectively changing the sign of each term.