If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. Got It The student provides complete and correct responses to all components of the task.
Provide additional opportunities for the student to write and solve absolute value equations. 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.
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.
Finds only one of the solutions of the first equation. Questions Eliciting Thinking Can you reread the first sentence of the second problem? Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?
This is the solution for equation 2. Should you use absolute value symbols to show the solutions? A difference is described between two values. Sciencing Video Vault 1.
What are these two values? Ask the student to solve the equation and provide feedback. 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.
What are the solutions of the first equation? Equation 2 is the correct one. To solve this, you have to set up two equalities and solve each separately. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
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: For a random number x, both the following equations are true: 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 Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
This means that any equation that has an absolute value in it has two possible solutions. This is solution for equation 1. Writes the solutions of the first equation using absolute value symbols.
Do you think you found all of the solutions of the first equation? You can now drop the absolute value brackets from the original equation and write instead: Emphasize that each expression simply means the difference between x and Plug these values into both equations.
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.
For example, represent the difference between x and 12 as x — 12 or 12 — x. Then explain why the equation the student originally wrote does not model the relationship described in the problem. What is the difference? Questions Eliciting Thinking How many solutions can an absolute value equation have?d) no real solutions e) -2, 2 More references and links on how to Solve Equations, Systems of Equations and Inequalities and Step by.
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 the difference between and 74 is six).
Provide additional opportunities for the student to write and solve absolute value equations. Almost There How many solutions can an absolute value equation have? Do. You can put this solution on YOUR website!
9 and 21 differ by Sinxe half of 12 is 6, we want the absolute value part to result in the values 6 and -6 in the equation. () Chapter 2 Linear Equations and Inequalities in One Variable The equation in the next example has an absolute value on both sides. EXAMPLE 4 Absolute value on both sides Solve 2x 1 x 3.
Solution Two quantities have the same absolute value only if they are equal or opposites. We're asked to solve for x. Let me just rewrite this equation so that the absolute values really pop out. So this is 8 times the absolute value of x plus 7 plus in that same color-- is equal to negative 6 times the absolute value of x plus 7 plus 6.
Solve an absolute value equation using the following steps: Get the absolve value expression by itself. Set up two equations and solve them separately.Download