Answer: Distance between O and the line 1 is 3 inches.
Explanation:
Since we have given that
Distance between point A and the line 1 = 10 inches
Distance between point B and the line 1 = 4 inches
Total length of segment AB is given by

Since O is midpoint of the line segment AB.
so, AO is given by

Now, Distance between O and the line 1 is given by

Hence, Distance between O and the line 1 is 3 inches.
The first step for absolute value equations is to isolate the expression contained within the absolute value bars:
3|2x+4|-1 = 11
3|2x+4| = 12
|2x+4| = 4
so |2x+4| is 4 units away from 0 on a number line, but we don't know in which direction -- negative or positive? you'll have two answers.
2x+4 = 4
AND
2x+4 = -4
solve both of those two step equations and you'll get
x = 0
AND
x = -4
so 0 and -4 are your solutions.
Max' brother is M-6 years old.
Since
are in arithmetic progression,




and since
are in geometric progression,




Recall that


It follows that

so the left side is

Also recall that

so that the right side is

Solve for
.

Now, the numerator increases more slowly than the denominator, since


and for
,

This means we only need to check if the claim is true for any
.
doesn't work, since that makes
.
If
, then

If
, then

If
, then

There is only one value for which the claim is true,
.