Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? What are these two values? Should you use absolute value symbols to show the solutions? Examples of Student Work at this Level The student correctly writes and solves the first equation: Instructional Implications Model using absolute value to represent differences between two numbers.
Examples of Student Work at this Level The student: Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
Provide additional opportunities for the student to write and solve absolute value equations. What is the difference? If needed, clarify the difference between an absolute value equation and the statement of its solutions. Do you think you found all of the solutions of the first equation?
Guide the student to write an equation to represent the relationship described in the second problem. 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 To solve this, you have to set up two equalities and solve each separately.
Then explain why the equation the student originally wrote does not model the relationship described in the problem. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.
You can now drop the absolute value brackets from the original equation and write instead: If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. Instructional Implications Provide feedback to the student concerning any errors made.For example, to solve the absolute value equation |4x + 5| = 13, you write the two linear equations and solve each for x: Both solutions work when you replace the x in the original equation with their values.
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.
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.
Writing an Absolute Value Function Write an equation of the graph shown. SOLUTION The vertex of the graph is (0, º3), so the equation has the form: y =a|x º 0|+(º3) or y = a|x| º 3 To find the value of a, substitute the coordinates of the point (2,1) into the equation and solve.
y = a|x| º 3 Write equation. 1 = a|2| º 3 Substitute 1 for y and 2 for x.
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Kuta Software - Infinite Algebra 2 Name_____ Solving Absolute Value Equations Date_____ Period____ Solve each equation.Download