Respuesta :
Inequality which ensure triangle exists is 22 > 4x > 7.
What is inequality ?
" Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Theorem used
In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get,
[tex]AB + BC > AC[/tex]
⇒[tex]2x + 4 + 6x > 18[/tex]
⇒[tex]8x > 18 - 4[/tex]
⇒ [tex]8x > 14[/tex]
⇒ [tex]4x > 7[/tex] ___(1)
[tex]AC + AB > BC[/tex]
⇒ [tex]18 + 2x + 4 > 6x[/tex]
⇒ [tex]22 > 6x-2x[/tex]
⇒[tex]22 > 4x[/tex] ____(2)
From (1) and (2) inequality of triangle we get,
[tex]22 > 4x > 7[/tex]
Hence, Inequality which ensure triangle exists is 22 > 4x > 7.
Learn more about inequality here
https://brainly.com/question/20383699
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