Absolute Value and Inequations

22 Absolute Value and Inequations

For $\quad b>0$ ,

$\bullet\qquad |a| < b \qquad \Longleftrightarrow\qquad -b< a < b$

ex.

$\qquad |x-5| < 3 \quad \Longleftrightarrow\quad -3<x-5< 3$

$\quad \Longleftrightarrow\quad -3+5 < x-5+ 5< 3+5 \quad\Longleftrightarrow \quad 2<x<8$

$\bullet\qquad |a| >b \quad\quad \qquad \Longleftrightarrow\qquad a<- b \quad\hbox{ or }\quad a >b$

ex.

$\qquad |x-5| >3 \qquad \Longleftrightarrow\qquad x-5< -3 \quad\hbox{ or }\quad x-5> 3$

$\qquad \qquad\Longleftrightarrow\qquad x<2\quad\hbox{ or }\quad x>8$

$\qquad \qquad\Longleftrightarrow\qquad x\in (-\infty, 2)\cup (8, +\infty)$

Watch a Video

View on YouTube

Exercise 1

Show/Hide Solution.

The set of possible solutions is the interval : $\qquad$ $I = \Big( 0, \displaystyle{\frac{1}{4}}\Big)$ .

Exercise 2

Show/Hide Solution.

The set of possible solutions is the interval : $\qquad$ $I = \Big( -\infty, -42\Big]\cup \Big[38, +\infty\Big)$ .

Exercise 3

Show/Hide Solution.

The set of possible solutions is the interval : $\qquad$ $I = \Big( 2, 6\Big)$ .

Icon for the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License