Examples of Student Work at this Level The student: Got It The student provides complete and correct responses to all components of the task. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.
Plug these values into both equations. Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.
What is the difference? Ask the student to solve the equation and provide feedback. You can now drop the absolute value brackets from the original equation and write instead: Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?
Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i. Examples of Student Work at this Level The student correctly writes and solves the first equation: When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
Questions Eliciting Thinking Can you reread the first sentence of the second problem? For example, represent the difference between x and 12 as x — 12 or 12 — x. Provide additional opportunities for the student to write and solve absolute value equations.
For a random number x, both the following equations are true: If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.
Then explain why the equation the student originally wrote does not model the relationship described in the problem.Solved: Write and absolute value equation that has the given solutions of x=3 and x=9 - Slader/5(1).
This absolute value equation is set equal to minus 8, a negative number.
By definition, the absolute value of an expression can never be negative. Hence, this equation has no solution. This means that any equation that has an absolute value in it has two possible solutions.
If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.
Solving Linear, Absolute Value and Quadratic Equations Basic Principle: If two things are equal, the results on performing the same operation on the two of them are equal. Linear Equations. Absolute value equations, quadratic equations and functions will help us solve an equation with absolute value.
The definition for the absolute value of a function is given by Solution: Using the definition of the absolute value of a function we can write, if.
Solving absolute value equations and inequalities. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. $$\left | x \right |.Download