Addition and subtraction equations up to 20: true or false?

Learning Objectives Define absolute value as a function representing distance from zero on a number line. Evaluate absolute value expressions that involve addition and subtraction with integers up to 20. Determine if a given value for a variable makes an absolute value equation a true or false statement. Solve absolute value equations of the form |ax + b| = c by isolating the absolute value expression and creating two distinct cases. Interpret the solutions to an absolute value equation as the values that make the statement true. Identify and avoid common algebraic errors when working with absolute value equations, such as improper distribution or forgetting the negative case. Connect the algebraic solutions of an absolute value equation to the intersection points on its gra...

TermDefinitionExample Absolute ValueThe distance of a number from zero on the number line. Since distance is always non-negative, the absolute value of any number is always non-negative.The absolute value of -9 is 9, written as `|-9| = 9`. The absolute value of 9 is also 9, written as `|9| = 9`. Absolute Value FunctionA function, typically written as f(x) = |x|, that outputs the absolute value of the input x. It is a V-shaped graph with its vertex at the origin.If f(x) = |x|, then f(-5) = |-5| = 5 and f(5) = |5| = 5. EquationA mathematical statement asserting that two expressions are equal, indicated by an equals sign (=).`|x - 4| + 3 = 10` is an equation. Truth ValueThe property of a statement being either true or false. In this context, we test if an equation is true for a specific valu...

The Absolute Value Equation Rule If `|E| = c` and `c > 0`, then `E = c` or `E = -c`. Use this rule after isolating the absolute value expression. It allows you to split a single absolute value equation into two separate, solvable linear equations. The Zero Property of Absolute Value If `|E| = 0`, then `E = 0`. If an absolute value expression equals zero, the expression inside the absolute value bars must also equal zero. This results in only one solution. The No Solution Rule for Absolute Value If `|E| = c` and `c < 0`, there is no solution. The result of an absolute value operation cannot be negative. If an absolute value expression is set equal to a negative number, the equation is always false and has no solution.