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.
This is the solution for equation 2. A difference is described between two values. 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 You can now drop the absolute value brackets from the original equation and write instead: For example, represent the difference between x and 12 as x — 12 or 12 — x.
Questions Eliciting Thinking Can you reread the first sentence of the second problem? What are the solutions of the first equation? Examples of Student Work at this Level The student: Equation 2 is the correct one.
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. Emphasize that each expression simply means the difference between x and Examples of Student Work at this Level The student correctly writes and solves the first equation: 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.
Got It The student provides complete and correct responses to all components of the task. To solve this, you have to set up two equalities and solve each separately. Do you think you found all of the solutions of the first equation?
What are these two values? Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? Guide the student to write an equation to represent the relationship described in the second problem.
If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. For a random number x, both the following equations are true: If needed, clarify the difference between an absolute value equation and the statement of its solutions.
Should you use absolute value symbols to show the solutions? Instructional Implications Provide feedback to the student concerning any errors made. Instructional Implications Model using absolute value to represent differences between two numbers.
Provide additional opportunities for the student to write and solve absolute value equations. Then explain why the equation the student originally wrote does not model the relationship described in the problem.
Plug these values into both equations. 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: Ask the student to solve the equation and provide feedback.
Questions Eliciting Thinking How many solutions can an absolute value equation have? Sciencing Video Vault 1.
This is solution for equation 1. What is the difference? Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.
Finds only one of the solutions of the first equation. This means that any equation that has an absolute value in it has two possible solutions.Want to write an equation to translate the graph of an absolute value equation?
This tutorial takes you through that process step-by-step! Take an absolute value equation and perform a vertical and horizontal translation to create. Writing Basic Absolute Value Equations Given the Graph Writing “y = |x – h| + k” Absolute Value Equations Given the Graph Solving Word Problems Involving Absolute Value Functions Overview Solving Word Problems by Graphing Absolute Value Functions Writing Absolute Value Functions — Writing Basic Absolute Value Equations.
Ask the student to solve the second equation and interpret the solutions in the context of the problem.
Ask the student to identify and write as many equivalent forms of the equation as possible. Then have the student solve each equation to show that they are equivalent.
Consider implementing MFAS task Writing Absolute Value Inequalities (A. Writing Equations of Absolute Value Functions. 3/29/ 3 Comments Match a given graph to its equation 3rd: Write the equation of function given its graph I feel that this order helps students complete the last task better.
For this matching game, I printed the solution page of the worksheet from kuta. The absolute number of a number a is written as $$\left | a \right |$$ And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression.
The equation $$\left | x \right |=a$$ Has two solutions x = a and x = -a because both numbers are at the distance a from 0. Because of how absolute values behave, it is important to include negative inputs in your T-chart when graphing absolute-value functions.
If you do not pick x-values that will put negatives inside the absolute value, you will usually mislead yourself as .Download