The goal of this two-day lesson was for students to build a deep understanding from a variety of different methods, and to be able to apply them to solve Absolute Value Equations and Inequalities. Students are usually more successful at solving Absolute Value Equations, but I did not want students to just memorize the procedure of solving Absolute Value Inequalities with no understanding. If students recognize a pattern based from the conceptual understanding and continue to apply it correctly, it is still different than memorizing.
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Free College algebra printable worksheets, how do you determine whether an integer is negative or positive when multiplying more than one integer, second order differential equation nonhomogeneous.Chapter 2 Linear Functions EXAMPLE 2 Solving Absolute-Value Equations Solve each equation.
A ⎪x-7⎥ = 5 This can be read as “the distance from x to 7 is 5.” x - 7 = 5 or x - 7 = -5 Rewrite the absolute value as a disjunction. x = 12 or x = 2 Add 7 to both sides of each equation. B ⎪3x⎥ + 5 = 14 ⎪3x⎥ = 9 Isolate the absolute-value expression.
3x = 9 or 3x = -9 Rewrite the. Compound Inequalities are two inequalities presented as one problem. The variable being solved for may need to only fulfill only one of the inequalities, or both, depending on if the word . an inequality that includes an absolute value; may have 2 solutions; you need to isolate the absolute value sign before you solve and set up two inequalities to solve absolute deviation The absolute deviation of a number x from a given value is the absolute value of the difference of x and the given value.
Write the absolute value inequality that corresponds to the following description: a) All the numbers that are less than 8 units away from 1 on the number line. b) All the numbers that are at least 6 units away from 2 on the number line. As you know, the absolute value functions have different expressions in different parts of the number line.
The strategy of solving such problems is to divide the number line in segments/intervals, where the absolute value functions can be written in more simple way, . In an inequality, one side of the inequality can be larger or smaller than the quantity on the other side. The math symbols, and ≥ provide information about the relative sizes of the two expressions.