Question

Point i is on line segment hj. Given hi=x, hj=3x-9, and ij=x+5, determine the numerical length of hj.

Answer 1

By setting up an equation based on the provided segments of a line, we find that the value of x is 14. Substituting this back into the expression for HJ, we determine that the numerical length of HJ is 33 units.

Step-by-step explanation:

We are given the following lengths on a line segment: HI = x, HJ = 3x - 9, and IJ = x + 5. To find the numerical length of HJ, we need to set up a relationship based on the fact that IJ is the difference between HJ and HI, meaning HJ = HI + IJ. Substituting the given expressions we have:
3x - 9 = x + (x + 5).

Solving this equation:

1. Combine like terms: 3x - 9 = 2x + 5.
2. Subtract 2x from both sides: x - 9 = 5.
3. Add 9 to both sides: x = 14.

Now that we have the value for x, we can substitute it back into the expression for HJ:

HJ = 3x - 9 = 3(14) - 9 = 42 - 9 = 33.

Therefore, the numerical length of HJ is 33 units.