Finding Absolute Value Inequality Statements

Slide 1: Finding absolute value inequality statements Copyright ©2007-2008 Home Tuition Services

Slide 2:We can show that if a≥0, −a ≤ x ≤ a ⇔ ∣ x ∣ ≤ a x ≤ −a or x ≥ a ⇔ ∣ x ∣ ≥ a .

Slide 3:Example 1 Find the absolute value inequality statement corresponding to x ≥ −3 or x ≤ 3 . ⇒ x ≥ −3 or x ≤ 3 ⇒ −3 ≤ x ≤ 3 We write in standard≤ form. ⇒ ∣ x ∣≤ 3 The statement is ∣ x ∣ ≤ 3

Slide 4:Example 2 Find the absolute value inequality statement corresponding to x ≤ 3 or x ≥ −3 . This is the same as Example 1 with the inequality statements in reverse order. Don't confuse this with statements x ≤ −3 or x ≥ 3 that lead to a standard ≥ absolute value inequality statement.

Slide 5:⇒ x ≤ 3 or x ≥ −3