Question

How do you write (-∞, 8) or (10, ∞) as an inequality?

Answer 1

Your answer would be, To write, (−∞,8), or (10,∞), ==> x < 8 or, x > 10

(-∞, 8) or (10, ∞)

Solution: ==> - 10 . ∞ + 8 . ∞ or, x < 8 or, x > 10

Steps:

(-∞, 8) or (10, ∞) ==> - 10 . ∞ + 8 . ∞

(-∞, 8) . (10, ∞)

Computing dot product of two Vectors:

( X1, Xn) . ( Y1, Yn) = Σ^n^i = 1X^iY^i

= ( - ∞) . 10 + 8 . ∞

Simplify:

( - ∞) 10 + 8 . ∞

- 10 . ∞ + 8 . ∞

( - ∞) . 10 + 8 . ∞

Remove Parenthesis:

( - a) ==> - a

- ∞ . 10 + 8 . ∞

==> - 10 . ∞ + 8 . ∞

==> (- 10 . ∞ + 8 . ∞) ==> - 10 . ∞ + 8 . ∞

( ==> - 10 . ∞ + 8 . ∞)

Remove Parenthesis:

( a) = a

==> - 10 . ∞ + 8 . ∞

Therefore, (-∞, 8) or (10, ∞) as an inequality, Answers are, ==>

- 10 . ∞ + 8 . ∞ or, x < 8 or, x > 10

Check:

(-∞, 8) or (10, ∞)

==> x < 8 or, x > 10

Solution:

x < 8 or, x > 10

Interval Notation:

[ x < 8 or, x > 10 ==> (-∞, 8) ∪ (10, ∞) ]

Steps:

x < 8 or, x > 10

x < 8 : x < 8

x < 8

x < 8

x < 8

x > 10 : x > 10

x > 10

x > 10

x > 10

Combine The Ranges:

x < 8, or x > 10

Hope that helps!!!!! : )