The answer in interval notation makes more sense if you see how it looks on the number line. 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?
When you take the absolute value of a number, the result is always positive, even if the number itself is negative. You might also be interested in: Emphasize that each expression simply means the difference between x and Do you think you found all of the solutions of the first equation?
If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.
Therefore, the answer is all real numbers. This statement must be false, therefore, there is no solution. This means that any equation that has an absolute value in it has two possible solutions.
What are these two values? Clear out the absolute value symbol using the rule and solve the linear inequality. For example, represent the difference between x and 12 as x — 12 or 12 — x. This is an example of case 3. 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: This is case 4.
We can also write the answer in interval notation using a parenthesis to denote that -8 and -4 are not part of the solutions. For a random number x, both the following equations are true: In case 2, the arrows will always be in opposite directions. Guide the student to write an equation to represent the relationship described in the second problem.
Instructional Implications Provide feedback to the student concerning any errors made. Instructional Implications Model using absolute value to represent differences between two numbers. Examples of Student Work at this Level The student: In case 2, the arrows will always point to opposite directions.
Provide additional opportunities for the student to write and solve absolute value equations.
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. It makes sense that it must always be greater than any negative number.
What do you get? Writes the solutions of the first equation using absolute value symbols. The shaded or closed circles signifies that -2 and 3 are part of the solution.
This will definitely help you solve the problems easily.
Ask the student to solve the equation and provide feedback. Or, write the answer on a number line where we use open circles to exclude -8 and -4 from the solution.
This is the solution for equation 2. Pick some test values to verify: What is the difference? Should you use absolute value symbols to show the solutions? The inequality symbol suggests that the solution are all values of x between -3 and 7, and also including the endpoints -3 and 7.
Then solve the linear inequality that arises. Solve the absolute value inequality.This tutorial shows you how to translate a word problem to an absolute value inequality.
Then see how to solve for the answer, write it in set builder notation, and graph it on a number line. Learn all about it in this tutorial! Case 2: Case 3: The absolute value of any number is either zero (0) or positive which can never be less than or equal to a negative number.
The answer to this case is always no solution. Case 4: The absolute value of any number is either zero (0) or positive. It makes sense that it must always be greater than any negative number.
Worked example: absolute value equation with two solutions Worked example: absolute value equations with one solution Worked example: absolute value equations with.
There absolute value word problems will teach how the absolute value can be used in the real world - Write an absolute value inequality that model your weight loss.
These 2 numbers are -2 and 4 of course since 4 - 1 = 3 and 1 - -2 = 3. And the two solutions (circled) are −7 and +3. Absolute Value Inequalities. Mixing Absolute Values and Inequalites needs a little care!
multiply by (1/3). Because we are multiplying by a positive number, the inequalities will not change: −2 ≤ x ≤ 6. Done! As an interval it can be written as: [−2, 6] Greater Than, Greater Than or.
Solving absolute value equations and inequalities. 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. Represents the distance between x and 0 that is greater than 2.
You can write an absolute value inequality as a compound inequality.Download