If two sides of a triangle have lengths 4 and 9 then the length of the third side may be any number a) greater than 5 but less than 13 b) greater than 4 but less than 9 c) greater than 15 d) less than 13

check the picture below.

on the first case, in green, if we lay the 4 side down flat on top of the 9 side, the lenght of "x" will be 9 - 4, or 5, however, we can't do that, because if we do, we end up with a flat-line and lose the triangle, so "x" can't be smaller than 5, it has to be larger than 5.

on the second case, if we lay the 4 side the other way flat on the ground, "x" will be of length 4 + 9, or 13, however, again, we can't do that, because if we do we'd lose our triangle again, so "x" can't be larger than 13, it has to be smaller than 13.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.