Question

In this exercise, let J is between H and K. Use the Segment Addition Postulate to solve for w. Find the length of each segment.

HJ=6w−5
IK=4w−6
KH=129

Answer 1

To solve for w using the Segment Addition Postulate, we can set up an equation using the lengths of the segments and then solve for w by isolating the variable.

Step-by-step explanation:

To solve for w using the Segment Addition Postulate, we can set up an equation using the lengths of the segments.

Given that HJ = 6w - 5, IK = 4w - 6, and KH = 129, we can write the equation as follows:

HJ + JK = KH

Substituting the given values, we have 6w - 5 + JK = 129. We can solve for w by isolating the variable:

6w + JK = 134

By substituting JK = 4w - 6 into the equation, we get:

6w + (4w - 6) = 134

Simplifying the equation, we can combine like terms:

10w - 6 = 134

Then we can solve for w by adding 6 to both sides of the equation:

10w = 140

Finally, dividing both sides by 10 gives us the value of w:

w = 14