How can you predict the sign of the sum answer before you actually do the math

see explanation

Step-by-step explanation:

first look at the abosloute value of the number, then go back to the question and look at the sign of that number. That sign should be the same sign as the sum.

for example

73+(-54)=

the absolute value of 73 is 73

the absolute value of -54 is 54

73 is bigger

go back to look at the sign of 73 in the eq.

it is positive, thus the answer should be positive too.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4