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.