Question

Need this problem solved with a step by step explanation. worth 50 points

Answer 1

LJ = 46

Explanation:

Given information:

• LK = MK
• LK = 7x - 10 ⇒ MK = 7x - 10
• KN = x + 3
• MN = 9x - 11
• KJ = 28

Segment Addition Postulate

If point B lies on the line segment AC, then AB + BC = AC.

Apply the Segment Addition Postulate to MN to find the value of x:

⇒ MN = MK + KN

⇒ 9x - 11 = 7x - 10 + x + 3

⇒ 9x - 11 = 7x + x - 10 + 3

⇒ 9x - 11 = 8x - 7

⇒ 9x - 11 - 8x = 8x - 7 - 8x

⇒ x - 11 = -7

⇒ x - 11 + 11 = -7 + 11

⇒ x = 4

Now we have found the value of x, we can calculate LJ, again applying the Segment Addition Postulate:

⇒ LJ = LK + KJ

⇒ LJ = 7x - 10 + 28

Substitute the found value of x into the equation:

⇒ LJ = 7(4) - 10 + 28

⇒ LJ = 28 - 10 + 28

⇒ LJ = 18 + 28

⇒ LJ = 46

Answer 2

• 46 units

Explanation:

According to segment addition postulate we have:

• MN = MK + KN and
• LJ = LK + KJ

Use the given values and find x:

• MN = LK + KN since MK = LK
• 9x - 11 = 7x - 10 + x + 3
• 9x - 11 = 8x - 7
• 9x - 8x = 11 - 7
• x = 4

Find LK:

• LK = 7*4 - 10 = 28 - 10 = 18

Find LJ:

• LJ = 18 + 28 = 46