Point J is between H and K on line segment HK. use th given information to write an equation in terms of x. Solve the equation. Then find HJ and JK.
HJ=(x/4)
JK= 3x - 4
KH = 22
clearly, HJ+JK=HK, so
x/4 + 3x-4 = 22
now just solve for x and evaluate the distances
ok, I got X = 2
is 2 correct for X?
To find HJ and JK, we first need to find the value of x by solving the equation given.
According to the problem, the lengths of the line segments are as follows: KH = 22, HJ = x/4, and JK = 3x - 4.
Since point J is between H and K on the line segment HK, the sum of HJ and JK must be equal to KH. Therefore, we can write the equation:
HJ + JK = KH
Replacing the lengths with their respective values:
(x/4) + (3x - 4) = 22
Now we can solve this equation for x:
(x/4) + 3x - 4 = 22
Multiply all terms by 4 to eliminate the fraction:
x + 12x - 16 = 88
Combine like terms:
13x - 16 = 88
Add 16 to both sides:
13x = 104
Divide both sides by 13:
x = 8
Now that we have the value of x, we can find the lengths of HJ and JK.
HJ = x/4 = 8/4 = 2
JK = 3x - 4 = 3(8) - 4 = 24 - 4 = 20
Therefore, HJ = 2 and JK = 20.