Question

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

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

Answer:

x = 3

TU = 35

UV = 35

TV = 70

Step-by-step 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