If TU = 3x-12 and SU = 4x + 2, find the value of x. Then find the length of TU and SU.

If ST= x + 3 and TU= 4x-6, find the value of x. Then find the length of ST and TU.

is there some relationship between TU and SU?

If they are congruent, then just solve

3x-12 = 4x+2

Since that gives a negative value for x, I think you need to clarify things a bit.

To find the value of x in the first question, we can set TU and SU equal to each other since they represent the same line:

3x - 12 = 4x + 2

By rearranging the equation, we can isolate the variable x:

3x - 4x = 2 + 12

-x = 14

x = -14

To find the length of TU and SU, substitute the value of x into the respective expressions:

For TU:
TU = 3x - 12
TU = 3(-14) - 12
TU = -42 - 12
TU = -54

For SU:
SU = 4x + 2
SU = 4(-14) + 2
SU = -56 + 2
SU = -54

Therefore, the length of TU and SU is both -54 units.

Similarly, in the second question, to find the value of x, we can set ST and TU equal to each other:

x + 3 = 4x - 6

By rearranging the equation, we can isolate the variable x:

x - 4x = -6 - 3

-3x = -9

x = 3

To find the length of ST and TU, substitute the value of x into the respective expressions:

For ST:
ST = x + 3
ST = 3 + 3
ST = 6

For TU:
TU = 4x - 6
TU = 4(3) - 6
TU = 12 - 6
TU = 6

Therefore, the length of ST and TU is both 6 units.