Distance between x and 8 is less than 14 write as an inequality

- 6 < x < 22

Step-by-step explanation:

|x-8| < 14

Then  x-8 < 14 and x-8 > -14.

If we consider the first one:

x-8 < 14

x < 22

Then the next one,

x-8 >-14

x > -6

You know have an upper and a lower limit for x: it must be larger than -6, and smaller than 22. So -6 < x < 22

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