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. This concept will play an important role as we solve absolute value equations. Provide additional opportunities for the student to write and solve absolute value equations.
And just think about that for a second. Absolute Value The absolute value of a number is its distance from 0 on the number line. If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. What are these two values? What are the solutions of the first equation?
What is the difference? For a random number x, both the following equations are true: Instructional Implications Provide feedback to the student concerning any errors made. This is the solution for equation 2.
Yes, there always has to be tricks, just to keep you on your toes. Guide the student to write an equation to represent the relationship described in the second problem. Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
There is no way that you can take the absolute value of a number and have a negative answer. Should you use absolute value symbols to show the solutions?
Questions Eliciting Thinking Can you reread the first sentence of the second problem? Therefore, if you come across an equation, such as the following: No absolute value can be a negative number.
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. However, this is not the only answer. Solving an Absolute Value Equation You must remember that when you are solving an absolute value equation, you will want to write two separate equations to solve.
When working with absolute value, think about what might not be possible If the answer to an absolute value equation is negative, then the answer is the empty set.
Sciencing Video Vault 1. So I want to get all of the absolute values of x plus 7 on the left-hand side, so I want to get rid of this one on the right-hand side. Distance can never be negative; therefore, the absolute value of a number is always positive.
For most absolute value equations, you will write two different equations to solve. The value inside of the absolute value can be positive or negative. So you could almost treat this expression-- the absolute value of x plus 7, you can just treat it as a variable, and then once you solve for that, it becomes a simpler absolute value problem.
What value can we substitute for x to get an answer of 4? 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.
Easiest way is to subtract 4 right over there, but if we do it on the left-hand side, we have to do it on the right-hand side as well.
This means that any equation that has an absolute value in it has two possible solutions. 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.How to find an equation given the absolute value graph?
Ask Question. Writing an equation for a log function given the graph. 5. How to graph this sin equation? 0. How do we know that a function's graph is an accurate representation of its solution set?
1. Graph of the equation 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.
The absolute value equation |ax + b| = c, where c > 0, is equivalent to the compound statement ax + b = c or ax + b = ºc. SOLVING AN ABSOLUTE VALUE EQUATION 5 4 3 2 1 0 The distance between 4 and 0 is 4, so | 4| 4. The distance between 4 and 0 is 4, so |4| 4. The distance between 0 and itself is 0, so |0| 0.
Solved: Write and absolute value equation that has the given solutions of x=3 and x=9 - Slader Search SEARCH. Scan; Browse upper level math high school math science social sciences literature and english foreign Write and absolute value equation that has the given solutions of x=3 and x=/5(1).
When you take the absolute value of a number, the result is always positive, even if the number itself is negative. For a random number x, both the following equations are true: |-x| = x and |x| = x.
This means that any equation that has an absolute value in it has two possible solutions. The student correctly writes both equations but errs in solving the first equation or writing its solutions. Examples of Student Work at this Level. The student: Finds only one of the solutions of the first equation.
Writes the solutions .Download