If needed, clarify the difference between an absolute value equation and the statement of its solutions. Examples of Student Work at this Level The student correctly writes and solves the first equation: Instructional Implications Provide feedback to the student concerning any errors made. Ask the student to solve the equation and provide feedback.
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? Then explain why the equation the student originally wrote does not model the relationship described in the problem.
To solve this, you have to set up two equalities and solve each separately. What are the solutions of the first equation? Should you use absolute value symbols to show the solutions? You can now drop the absolute value brackets from the original equation and write instead: For a random number x, both the following equations are true: Guide the student to write an equation to represent the relationship described in the second problem.
This is solution for equation 1. Do you think you found all of the solutions of the first equation? 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. Writes the solutions of the first equation using absolute value symbols.
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?
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.
Sciencing Video Vault 1. What is the difference? Emphasize that each expression simply means the difference between x and 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. Questions Eliciting Thinking How many solutions can an absolute value equation have?
Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? Plug these values into both equations. Examples of Student Work at this Level The student: 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 For example, represent the difference between x and 12 as x — 12 or 12 — x.
What are these two values? Provide additional opportunities for the student to write and solve absolute value 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: Equation 2 is the correct one.
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.
A difference is described between two values.This equation has parentheticals on both sides of the equation. take your time and write out all of your steps, like I did above.
Don't try to do everything in your head. because you can always check your answer. The meaning of the solution value is that it is the x-value that makes the equation true.
So, to check your answer, you plug. Absolute Value Equation Equivalent Equation Solution Set x k (k 0) x k or x k k, k x 0 x 0 0 x k (k 0) There is no solution because no number has a negative absolute value. Absolute Value Equations and Inequalities () 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. 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 |. Beyond Standards Math K-5 Videos; Assessments; Original Student Tutorials; Provide additional opportunities for the student to write and solve absolute value equations. Almost There: Why was it necessary to use absolute value to write this equation?
How many solutions do you think this equation has? Why are there two solutions?
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 .Download