If T is the midpoint of SU,find x. ( ST=8x+11 and TU= 12x-1)

Answer:

Step-by-step explanation:

To find x, set the two expressions equal and solve:

8x + 11 = 12x - 1

11 = 4x - 1

12 = 4x

x = 3

Answer: x = 3

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Explanation:

Since T is the midpoint of segment SU, it divides SU into two equal parts, which means ST equals TU.

Set ST equal to TU:

8x + 11 = 12x - 1

Subtract 8x from both sides:

11 = 4x - 1

Add 1 to both sides:

12 = 4x

Divide both sides by 4:

x = 3

To verify, substitute x = 3:

ST = 8(3) + 11 = 24 + 11 = 35

TU = 12(3) - 1 = 36 - 1 = 35

Both segments are equal to 35 units, confirming the solution is correct.