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Answer :

Given:

The inequality is given as,

[tex]-6>x^2+4x[/tex]

The objective is to solve the inequality algebraically.

Explanation:

By adding +4 on both sides of the equation,

[tex]4-6>x^2+4x+4[/tex]

Now, by rearranging the above equation,

[tex]-2>x^2+2(2)x+2^2[/tex]

Using algebraic identity,

[tex]-2>(x+2)^2\text{ . . . . . (1)}[/tex]

If n is even in a term aⁿ, then the value of the term must be greater than zero.

By consider the equation (1), the degree is 2 in the term (x+2)², then the term must be greater than zero. But the inequality represents that the value is lesser than -2.

Hence, the given inequality has no solution.