1. ac = 95, ab = 15x - 10, bc = 5x + 5
2. ac = 8x - 16, ab = 3x - 8, bc = 4x
3. ac = x - 0.4, ab = x - 4.9, bc = 0.5x
4. ac = 383, ab = 6x, bc = 8x + 1

Part 1) x=5, AB=65 units, BC=30 units

Part 2) x=8, AB=16 units, BC=32 units

Part 3) x=9, AB=4.1 units, BC=4.5 units

Part 4) x=2 3/4, AB=16 1/2 units, BC=22 1/4 units

Step-by-step explanation:

The complete question in the attached figure

we have that

Point B is between A and C on segment AC

we know that

-----> equation A (by addition segment postulate)

Part 1) we have

AC = 95, AB = 15x - 10, BC = 5x + 5

substitute the given values in equation A and solve for x

Combine like terms in the right side

Adds 5 both sides

Divide by 20 both sides

Rewrite

Find the value of AB

substitute the value of x

Find the value of BC

substitute the value of x

Part 2) we have

AC = 8x - 16, AB = 3x - 8, BC = 4x

substitute the given values in equation A and solve for x

Combine like terms in the right side

Adds 16 both sides

Subtract 7x both sides

Find the value of AB

substitute the value of x

Find the value of BC

substitute the value of x

Part 3) we have

AC = x - 0.4, AB = x - 4.9, BC = 0.5x

substitute the given values in equation A and solve for x

Combine like terms in the right side

Adds 4.9 both sides

Subtract x both sides  

Divide by 0.5 both sides

Rewrite

Find the value of AB

substitute the value of x

Find the value of BC

substitute the value of x

Part 4) we have

AC = 38 3/4, AB = 6x, BC = 8x + 1/4

substitute the given values in equation A and solve for x

Convert mixed number to an improper fraction

substitute

Multiply by 4 both sides to remove the fraction

Combine like terms in the right side

Subtract 1 both sides

Divide by 56 both sides

Rewrite

Simplify

Rewrite x as mixed number

Find the value of AB

substitute the value of x

Rewrite AB as mixed number

Find the value of BC

substitute the value of x

51-50

step-by-step explanation:

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step-by-step explanation: