Question

Let $x,x+1,x+2$, be the lengths of the three sides of a triangle.
(i) Write down the three inequations in x, each of which represents the given statement.
(ii) List the set of possible values of x which satisfy all the three inequations obtained in your answer to part (i) above, given that x is an integer.

Answer 1

$\left(i\right)x+(x+1)>(x+2)$

$=>2x+1>x+2$

$=>x>1-\left(1\right)$

$(x+1)+(x+2)>x$

$=>2x+3>x$

$=>x>-3-\left(2\right)$

$x+(x+2)>x+1$

$=>2x+2>x+1$

$=>x>-1-\left(3\right)$

$\left(1\right)\left(2\right)\&\left(3\right)representthethreeinequalities$

$\left(ii\right)comparing\left(1\right),\left(2\right)\&\left(3\right)$

$=>x>-3$

$x>-1$

$x>1$

$\therefore x>1$

$\therefore possiblevaluesofx=2,3,4,5,6,......$