Question

(Giving 75 points! Please do not answer without showing work and do not answer if you do not know the answer.)

Since we know U is the midpoint, we can say TU=
substituting in our values for each we get:

? =12x−1

Solve for x
We now want to solve for x.

−4x+11=−1

−4x= ?

x= 3


Solve for TU, UV, and TV
This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(?)+11

TU= ?

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Using the segment addition postulate we know:

TU+UV=TV

35+35=TV

TV= 70

Answer 1

• 8x+11=12x-1
• 11+1=12x-8x
• 4x=12
• x=3

Hence

• TU=8(3)+11=35
• UV=12(3)-1=35
• TV=2(35)=70

Answer 2

x = 3

TU = 35

UV = 35

TV = 70

Explanation:

As U is the midpoint of TV:

⇒ TU = UV

⇒ 8x + 11 = 12x - 1

⇒ 8x + 11 - 11 = 12x - 1 - 11

⇒ 8x = 12x - 12

⇒ 8x - 12x = 12x - 12 - 12x

⇒ -4x = -12

⇒ -4x ÷ -4 = -12 ÷ -4

⇒ x = 3

Substitute the found value of x into the expression for TU:

⇒ TU = 8x + 11

⇒ TU = 8(3) + 11

⇒ TU = 24 + 11

⇒ TU = 35

Using the transitive property of equality:

As UV = TU and TU = 15 then UV = 35

Using the segment addition postulate:

⇒ TV = TU + UV

⇒ TV = 35 + 35

⇒ TV = 70