What is the difference? For a random number x, both the following equations are true: Questions Eliciting Thinking How many solutions can an absolute value equation have?
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
Examples of Student Work at this Level The student: Instructional Implications Model using absolute value to represent differences between two numbers. You can now drop the absolute value brackets from the original equation and write instead: When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
This is the solution for equation 2. If needed, clarify the difference between an absolute value equation and the statement of its solutions. Plug these values into both equations.
Should you use absolute value symbols to show the solutions? Guide the student to write an equation to represent the relationship described in the second problem.
Then explain why the equation the student originally wrote does not model the relationship described in the problem. What are these two values? What are the solutions of the first equation? Equation 2 is the correct one. Do you think you found all of the solutions of the first equation?
A difference is described between two values.
Questions Eliciting Thinking Can you reread the first sentence of the second problem? This is solution for equation 1. Examples of Student Work at this Level The student correctly writes and solves the first equation: 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 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.
Ask the student to solve the equation and provide feedback. Sciencing Video Vault 1. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.
If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. To solve this, you have to set up two equalities and solve each separately. Provide additional opportunities for the student to write and solve absolute value equations.
This means that any equation that has an absolute value in it has two possible solutions. Got It The student provides complete and correct responses to all components of the task. Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?
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.
Emphasize that each expression simply means the difference between x and For example, represent the difference between x and 12 as x — 12 or 12 — x. Writes the solutions of the first equation using absolute value symbols. 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.
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: Instructional Implications Provide feedback to the student concerning any errors made. 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.
If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and. Absolute Value Equations Discussion: Absolute value refers to the measure of distance from zero for any value on the number line.
For example, the absolute value of 3 is 3 (written as) because there are three units between the. Aug 21, · Best Answer: Sometimes, when you look at a graph of an equation, you can look at it and see two or more clearly defined "pieces".
For example, perhaps part of the equation looks like a line, and another part looks like half of a parabola. That's what "piecewise" is mint-body.com: Resolved. 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. 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.
Sep 06, · This algebra video tutorial shows you how to solve absolute value equations with inequalities and how to plot the solution on a number line and write the answer in interval notation.
This video also shows you how to identify cases of no solution or infinitely many solutions / all solutions.Download