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Absolute Value Equations and Inequalities. Absolute Value Definition - The absolute value of x, is defined as... = , ≥ 0 −, < 0 where x is called the “argument”.
To handle the absolute value, we must break the problem into cases: We know that the argument x 1 of the absolute value is non-negative when x 1. In this case, the inequality reduces to x 1 x; which always holds. The solutions set for this case is thus [1;1). In the remaining case, where x<1, the inequality becomes x+ 1 x;
The absolute value function is commonly used to determine the distance between two numbers on the number line. Given two values a and b, then a − b will give the distance, a positive quantity, between these values, regardless of which value is larger.
1.6 Practice - Absolute Value Equations Solve each equation. 1) |x|=8 3) |b|=1 5) |5+8a|=53 7) |3k+8|=2 9) |9+7x|=30 11) |8+6m|=50 13) |6−2x|=24 15) −7|−3−3r|=−21 17) 7|−7x−3|=21 19) |−4b−10| 8 =3 21) 8|x+7|−3=5 ... Answers to Absolute Value Equations 1) 8, −8 2) 7,−7
In this section, we will investigate absolute value functions. Understanding Absolute Value . Recall that in its basic form f (x) = | x |, f (x) = | x |, the absolute value function, is one of our toolkit functions. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line ...
Absolute value inequalities can be solved using the basic concept underlying the property of absolute value equalities. Whereas the equation asks for all numbers
23 mar 2024 · Another way to define absolute value is by the equation \(|x| = \sqrt{x^2}\). Using this definition, we have \(|5| = \sqrt{(5)^2} = \sqrt{25} = 5\) and \(|-5| = \sqrt{(-5)^2} = \sqrt{25} = 5\). The long and short of both of these procedures is that \(|x|\) takes negative real numbers and assigns them to their positive counterparts while it ...
