Question

Solve the inequality -

0.5 / x - x² - 1 < 0

Answer 1

★ INEQUALITIES ★

0.5 / x - x² - 1 < 0

0.5 / - 1 ( x² - x + 1 ) < 0

Hence ,

x ∈ ( - ∞ , + ∞ )

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Answer 2

Concept:

"A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."

For instance, x>3 (x should be greater than 3)

If there is just one variable, the inequality is said to have an open sentence.

Instance: x 6 (x is less than 6)

Double Inequalities: If the statement demonstrates a double relation between the expressions or the numbers, the inequality is said to be a double inequality.

Instance: 3 x 8 ( x is greater than or equal to 3 and less than 8)

Expressions with linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values could be either numerical, algebraic, or both. Examples of numerical inequality include 1011 and 20>17, whereas algebraic inequalities include x>y, y>19-x, and x z > 11 (also called literal inequalities)

Given:

0.5 / x - x² - 1 < 0

Find:

Find the range of x

Solution:

0.5 / x - x² - 1 < 0

∵x - x² - 1 is always negative and 0.5 is a constant no.

So we can write,

x∈(-∞,∞) or x∈R

Therefore, x∈(-∞,∞) or x∈R

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